[TERLENGKAP] Inilah Contoh-contoh Rumus Matematika dengan Math Input di Wolfram Alpha (Part 2)

Assalamu‘alaikum wr. wb.

Hello guys! Jika sebelumnya sudah sedikit dibahas tentang Rumus-rumus Matematika menggunakan Math Input di Wolfram|Alpha di Part 1, sekarang kita akan melanjutkan kembali tentang Input-an Rumus Matematika di Wolfram Alpha. Jika di Part 1 membahas tentang Matematika Dasar, Aljabar, dan Fungsi, sekarang kita akan menyambung Topik tentang Vektor dan Matriks, Prakalkulus, Kalkulus, sampai dengan Transformasi.

Sumber Utama : Wikipedia.org (Sebagian), Wolframalpha.com (Math Input), dan Wolfram.com (Blog) [Lalu diterjemahkan melalui Google Translate]

Sumber Rumus-rumus : Wolfram|Alpha Math, Microsoft Math Solver, dan Symbolab.com

CONTOH INPUT MATEMATIKA LANJUTAN DI WOLFRAM ALPHA

Dan berikut, inilah Contoh-contoh Inputan Rumus Matematika di Wolfram|Alpha dari yang Sederhana hingga yang tersulit.

D. Vektor dan Matriks

Yaitu Notasi Array/Larik yang terdiri dari Baris dan Kolom. Untuk Vektor biasanya m×1 dan Matriks terdiri dari m×n. Akan tetapi, untuk Persamaan 2 Variabel atau lebih juga bisa menggunakan Vektor untuk mengekspresikan persamaannya. Dan juga untuk Piecewise juga bisa ditambahkan ke dalam bagian ini. Adapun penggunaan Piecewise adalah untuk penggunaan Fungsi Kekontinuan.

1. Vektor Sederhana

  

(2, 3)

Wolfram Language and Alternate :
{2,3} or (2, 3)
Math Input :
Klik di sini

Wolfram Language and Alternate :
{{2},{3}}
Math Input :
Klik di sini

  

(2, 3, 4)

Wolfram Language and Alternate :
{2,3,4} or (2, 3, 4)
Math Input :
Klik di sini

Wolfram Language and Alternate :
{{2},{3},{4}}
Math Input :
Klik di sini

  

(a, b, c, d)

Wolfram Language and Alternate :
{a,b,c,d} or (a, b, c, d)
Math Input :
Klik di sini

Wolfram Language and Alternate :
{{a},{b},{c},{d}}
Math Input :
Klik di sini

2. Operasi Hitung Vektor

(5, 2) + (-2, 3)

Wolfram Language and Alternate :
{5,2}+{-2,3} or (5, 2) + (-2, 3)
Math Input :
Klik di sini

Wolfram Language and Alternate :
{{5},{2}}+{{-2},{3}}
Math Input :
Klik di sini

(1, 4, 3) + 2(3, 6, 7)

Wolfram Language and Alternate :
{1,4,3}+2{3,6,7} or (1, 4, 3) + 2(3, 6, 7)
Math Input :
Klik di sini

Wolfram Language and Alternate :
{{1},{4},{3}}+2{{3},{6},{7}}
Math Input :
Klik di sini

(4, 2, -3, 6) + 3(1, -1, 4, 0)

Wolfram Language and Alternate :
{4,2,-3,6}+3{1,-1,4,0} or (4, 2, -3, 6) + 3(1, -1, 4, 0)
Math Input :
Klik di sini

Wolfram Language and Alternate :
{{4},{2},{-3},{6}}+3{{1},{-1},{4},{0}}
Math Input :
Klik di sini

3(2, 3) - (4, -1)

Wolfram Language and Alternate :
3{2,3}-{4,-1} or 3(2, 3) - (4, -1)
Math Input :
Klik di sini

Wolfram Language and Alternate :
3{{2},{3}}-3{{4},{-1}}
Math Input :
Klik di sini

2(-6, 14, 7) - (11, -3, 9)

Wolfram Language and Alternate :
2{-6,14,7}-{11,-3,9} or 2(-6, 14, 7) - (11, -3, 9)
Math Input :
Klik di sini

Wolfram Language and Alternate :
2{{6},{14},{7}}-{{11},{-3},{9}}
Math Input :
Klik di sini

7(1, 0, -2, 1) - 4(2, -1, 1, -3)

Wolfram Language and Alternate :
7{1,0,-2,1}-4{2,-1,1,-3} or 7(1, 0, -2, 1) - 4(2, -1, 1, -3)
Math Input :
Klik di sini

Wolfram Language and Alternate :
7{{1},{0},{-2},{1}}-4{{2},{-1},{1},{-3}}
Math Input :
Klik di sini

(2, 4)*(5, 3)

Wolfram Language and Alternate :
{2,4}*{5,3} or (2, 4)*(5, 3)
Math Input :
Klik di sini

(1, 2, 3)*(7, 5, 4)

Wolfram Language and Alternate :
{1,2,3}*{7,5,4} or (1, 2, 3)*(7, 5, 4)
Math Input :
Klik di sini

(-2, 4, 10, 5)*(12, 4, -1, 2)

Wolfram Language and Alternate :
{-2,4,10,5}*{12,4,-1,2} or (-2, 4, 10, 5)*(12, 4, -1, 2)
Math Input :
Klik di sini

3. Persamaan Linear 2 Variabel

Wolfram Language and Alternate :
{2x+3y=8, 3x+y=5}
Math Input :
Klik di sini

Wolfram Language and Alternate :
{3x+5y=21, 2x–7y=45}
Math Input :
Klik di sini

Wolfram Language and Alternate :
{-2x+3y=16, 5x–4y=-6}
Math Input :
Klik di sini

Wolfram Language and Alternate :
{x+y=10, xy=25}
Math Input :
Klik di sini

Wolfram Language :
{Divide[x,y]=3, x-y=15}
Alternate :
{x/y=3, x-y=15}
Math Input :
Klik di sini

Wolfram Language :
{x+Divide[y,3]=6, Divide[x,2]+2Divide[y,3]=9}
Alternate :
{x+y/3=6, x/2+2y/3=9}
Math Input :
Klik di sini

Wolfram Language :
{2x-Divide[y,5]=5, Divide[x,3]+5Divide[y,4]=4}
Alternate :
{2x-y/5=5, x/3+5y/4=4}
Math Input :
Klik di sini

4. Pertidaksamaan Linear 2 Variabel

Wolfram Language and Alternate :
{2x+3y>6, 4x-y<9}
Math Input :
Klik di sini

Wolfram Language :
{Divide[x,2]+y≥2, Divide[x-2y,3]≤1}
Alternate :
{x/2+y≥2, (x-2y)/3≤1} or {x/2+y>=2, (x-2y)/3<=1}
Math Input :
Klik di sini

Wolfram Language and Alternate :
{x+y≤9, 6x+11y≤66, x≥0, y≥0} or {x+y<=9, 6x+11y<=66, x>=0, y>=0}
Math Input :
Klik di sini

Wolfram Language and Alternate :
{x+y≤5, 4x+6y≤24, x≥1, y≥2} or {x+y<=5, 4x+6y<=24, x>=1, y>=2}
Math Input :
Klik di sini

Wolfram Language :
{2x-Divide[y,2]≤16, Divide[4x,3]+y≥3, x<0, y>1}
Alternate :
{2x-y/2≤16, 4x/3+y≥3, x<0, y>1} or {2x-y/2<=16, 4x/3+y>=3, x<0, y>1}
Math Input :
Klik di sini

5. Persamaan Linear 3 Variabel

Wolfram Language and Alternate :
{x-3y+z=8, 2x+3y-z=5, 3x-2y-2z=7}
Math Input :
Klik di sini

Wolfram Language and Alternate :
{2x+y-3z=6, x-3y+3z=-2, -3x+2y-z=3}
Math Input :
Klik di sini

Wolfram Language :
{Divide[1,x]+Divide[3,y]+Divide[1,z]=Divide[7,3], Divide[-2,x]+Divide[1,y]-Divide[1,z]=Divide[3,4], Divide[3,x]-Divide[1,y]+Divide[2,z]=5}
Alternate :
{1/x+3/y+1/z=7/3, -2/x+1/y-1/z=3/4, 3/x-1/y+2/z=5}
Math Input :
Klik di sini

6. Matriks Sederhana

[[2,-4],[3,5]]

Wolfram Language and Alternate :
{{2,-4},{3,5}} or [[2,-4],[3,5]]
Math Input :
Klik di sini

[[2,5,8],[x,4,y],[1,3,7]]

Wolfram Language and Alternate :
{{2,5,8},{x,4,y},{1,3,7}} or [[2,5,8],[x,4,y],[1,3,7]]
Math Input :
Klik di sini

[[2,3,4],[1,5,6]]

Wolfram Language and Alternate :
{{2,3,4},{1,5,6}} or [[2,3,4],[1,5,6]]
Math Input :
Klik di sini

[[3,-4],[-2,1],[-5,6]]

Wolfram Language and Alternate :
{{3,-4},{-2,1},{-5,6}} or [[3,-4],[-2,1],[-5,6]]
Math Input :
Klik di sini

7. Fungsi pada Matriks

[[2,-1],[1,4]]^T

Wolfram Language :
Transpose{{2,-1},{1,4}}
Alternate :
transpose{{2,-1},{1,4}} or Transpose[[2,-1],[1,4]] or {{2,-1},{1,4}}^T or [[2,-1],[1,4]]^T
Math Input :
Klik di sini

[[1,2,3],[4,5,6],[7,8,9]]^T

Wolfram Language :
Transpose{{1,2,3},{4,5,6},{7,8,9}}
Alternate :
transpose{{1,2,3},{4,5,6},{7,8,9}} or Transpose[[1,2,3],[4,5,6],[7,8,9]] or {{1,2,3},{4,5,6},{7,8,9}}^T or [[1,2,3],[4,5,6],[7,8,9]]^T
Math Input :
Klik di sini

adj[[2,-1],[1,4]]

Wolfram Language :
Adjugate{{2,-1},{1,4}}
Alternate :
adjugate{{2,-1},{1,4}} or adjugate[[2,-1],[1,4]]
Math Input :
Klik di sini

adj[[8,7,9],[6,6,2],[5,7,9]]

Wolfram Language :
Adjugate{{8,7,9},{6,6,2},{5,7,9}}
Alternate :
adjugate{{8,7,9},{6,6,2},{5,7,9}} or adjugate[[8,7,9],[6,6,2],[5,7,9]]
Math Input :
Klik di sini

det[[4,2],[5,6]]

Wolfram Language :
Determinant{{4,2},{5,6}}
Alternate :
determinant{{4,2},{5,6}} or det{{4,2},{5,6}} or det[[4,2],[5,6]]
Math Input :
Klik di sini

det[[9,2,-3],[-6,7,5],[1,-8,4]]

Wolfram Language :
Determinant{{9,2,-3},{-6,7,5},{1,-8,4}}
Alternate :
determinant{{9,2,-3},{-6,7,5},{1,-8,4}} or det{{9,2,-3},{-6,7,5},{1,-8,4}} or det[[9,2,-3],[-6,7,5],[1,-8,4]]
Math Input :
Klik di sini

det[[-14,2,13,-9],[4,-8,12,6],[-4,16,0,-6],[15,7,11,10]]

Wolfram Language :
Determinant{{-14,2,13,-9},{4,-8,12,6},{-4,16,0,-6},{15,7,11,10}}
Alternate :
determinant{{-14,2,13,-9},{4,-8,12,6},{-4,16,0,-6},{15,7,11,10}} or det{{-14,2,13,-9},{4,-8,12,6},{-4,16,0,-6},{15,7,11,10}} or det[[-14,2,13,-9],[4,-8,12,6],[-4,16,0,-6],[15,7,11,10]]
Math Input :
Klik di sini

[[4,2],[5,3]]^-1

Wolfram Language :
Inverse{{4,2},{5,3}}
Alternate :
inverse{{4,2},{5,3}} or inv{{4,2},{5,3}}
Math Input :
Klik di sini

[[10,-9,-12],[-7,11,8],[5,6,13]]^-1

Wolfram Language :
Inverse{{10,-9,-12},{-7,11,8},{5,6,13}}
Alternate :
inverse{{10,-9,-12},{-7,11,8},{5,6,13}} or inv{{10,-9,-12},{-7,11,8},{5,6,13}}
Math Input :
Klik di sini

[[9,2,-12,3],[-7,1,11,8],[5,4,6,13],[-1,13,2,0]]^-1

Wolfram Language :
Inverse{{9,2,-12,3},{-7,1,11,8},{5,4,6,13},{-1,13,2,0}}
Alternate :
inverse{{9,2,-12,3},{-7,1,11,8},{5,4,6,13},{-1,13,2,0}} or inv{{9,2,-12,3},{-7,1,11,8},{5,4,6,13},{-1,13,2,0}}
Math Input :
Klik di sini

https://www.wolframalpha.com/examples/mathematics/linear-algebra/matrices

8. Operasi Hitung Matriks

[[2,-1],[1,4]]+[[5,2],[2,1]]

Wolfram Language and Alternate :
{{2,-1},{1,4}}+{{5,2},{2,1}} or [[2,-1],[1,4]]+[[5,2],[2,1]]
Math Input :
Klik di sini

[[3,8],[-1,3]]-[[4,-2],[4,5]]

Wolfram Language and Alternate :
{{3,8},{-1,3}}-{{4,-2},{4,5}} or [[3,8],[-1,3]]-[[4,-2],[4,5]]
Math Input :
Klik di sini

[[1,4,8],[5,-7,6],[-3,8,9]]+[[9,-2,5],[-3,6,-8],[7,4,1]]

Wolfram Language and Alternate :
{{1,4,8},{5,-7,6},{-3,8,9}}+{{9,-2,5},{-3,6,-8},{7,4,1}} or [[1,4,8],[5,-7,6],[-3,8,9]]+[[9,-2,5],[-3,6,-8],[7,4,1]]
Math Input :
Klik di sini

[[1,2,3],[5,14,6],[9,8,10]]-[[-5,2,0],[7,3,-4],[-1,4,2]]

Wolfram Language and Alternate :
{{1,2,3},{5,14,6},{9,8,10}}-{{-5,2,0},{7,3,-4},{-1,4,2}} or [[1,2,3],[5,14,6],[9,8,10]]-[[-5,2,0],[7,3,-4],[-1,4,2]]
Math Input :
Klik di sini

2[[4,2],[3,5]]

Wolfram Language and Alternate :
2{{4,2},{3,5}} or 2[[4,2],[3,5]]
Math Input :
Klik di sini

3[[12,8,3],[5,3,6],[9,4,10]]

Wolfram Language and Alternate :
3{{12,8,3},{5,3,6},{9,4,10}} or 3[[12,8,3],[5,3,6],[9,4,10]]
Math Input :
Klik di sini

[[4,3],[5,6]]*[[4],[3]]

Wolfram Language and Alternate :
{{4,3},{5,6}}*{{4},{3}} or [[4,3],[5,6]]*[[4],[3]]
Math Input :
Klik di sini

[[3,2,6],[4,3,0],[7,4,8]]*[[8],[5],[9]]

Wolfram Language and Alternate :
{{3,2,6},{4,3,0},{7,4,8}}*{{8},{5},{9}} or [[3,2,6],[4,3,0],[7,4,8]]*[[8],[5],[9]]
Math Input :
Klik di sini

[[3,6,1],[2,-4,6],[8,4,0]]*[[0,3],[-1,5],[2,-4]]

Wolfram Language and Alternate :
{{3,6,1},{2,-4,6},{8,4,0}}*{{0,3},{-1,5},{2,-4}} or [[3,6,1],[2,-4,6],[8,4,0]]*[[0,3],[-1,5],[2,-4]]
Math Input :
Klik di sini

[[1,-2],[-3,4]]*[[5,4,9],[7,8,1]]

Wolfram Language and Alternate :
{{1,-2},{-3,4}}*{{5,4,9},{7,8,1}} or [[1,-2],[-3,4]]*[[5,4,9],[7,8,1]]
Math Input :
Klik di sini

[[2,-1],[0,3]]*[[5,6],[-3,4]]

Wolfram Language and Alternate :
{{2,-1},{0,3}}*{{5,6},{-3,4}} or [[2,-1],[0,3]]*[[5,6],[-3,4]]
Math Input :
Klik di sini

[[1,10,8],[5,-6,7],[-3,8,-9]]*[[9,-2,5],[-3,7,-8],[6,9,4]]

Wolfram Language and Alternate :
{{1,10,8},{5,-6,7},{-3,8,-9}}*{{9,-2,5},{-3,7,-8},{6,9,4}} or [[1,10,8],[5,-6,7],[-3,8,-9]]*[[9,-2,5],[-3,7,-8],[6,9,4]]
Math Input :
Klik di sini

https://www.wolframalpha.com/examples/mathematics/algebra/matrices

9. Piecewise Function

Wolfram Language :
f(x) = Piecewise[{{Power[x,2],x>1},{x-1,x≤1}}]
Alternate :
f(x) = Piecewise[{{x^2,x>1},{x-1,x≤1}}]
Math Input :
Klik di sini

Wolfram Language :
g(x) = Piecewise[{{-x,x<0},{1-Power[x,2],x≥0}}]
Alternate :
g(x) = Piecewise[{{-x,x<0},{1-x^2,x≥0}}]
Math Input :
Klik di sini

Wolfram Language :
h(x) = Piecewise[{{1+x,x<0},{1-Power[x,2],x>0}}]
Alternate :
h(x) = Piecewise[{{1+x,x<0},{1-x^2,x>0}}]
Math Input :
Klik di sini

Wolfram Language :
k(x) = Piecewise[{{Sqrt[x+1],x≥-1},{-x-1,x<-1}}]
Alternate :
k(x) = Piecewise[{{sqrt(x+1),x≥-1},{-x-1,x<-1}}] or k(x) = Piecewise[{{√(x+1),x≥-1},{-x-1,x<-1}}]
Math Input :
Klik di sini

Wolfram Language :
h(x) = Piecewise[{{3Power[x,2],x≥0},{4x,x≤0}}]
Alternate :
h(x) = Piecewise[{{3x^2,x≥0},{4x,x≤0}}]
Math Input :
Klik di sini

Wolfram Language :
f(x) = Piecewise[{{Power[x,2]-1,x≤-1},{2x+2,x>-1}}]
Alternate :
f(x) = Piecewise[{{x^2-1,x≤-1},{2x+2,x>-1}}]
Math Input :
Klik di sini

Wolfram Language :
g(x) = Piecewise[{{Divide[Power[x,3]-4x,x-2],x≠2},{2x+2,x=2}}]
Alternate :
g(x) = Piecewise[{{(x^3-4x)/(x-2),x≠2},{8,x=2}}]
Math Input :
Klik di sini

Wolfram Language :
f(x) = Piecewise[{{3+Power[x,2],x≤0},{Divide[Sin[3x],x],x>0}}]
Alternate :
f(x) = Piecewise[{{3+x^2,x≤0},{sin⁡(3x)/x,x>0}}]
Math Input :
Klik di sini

Wolfram Language and Alternate :
f(x) = Piecewise[{{x+1,x<3},{2,x=3},{7-x,x>3}}]
Math Input :
Klik di sini

Wolfram Language :
g(x) = Piecewise[{{2x+2,x≤-1},{Divide[3x,4],-1<x≤2},{Power[e,x-2],x>2}}]
Alternate :
g(x) = Piecewise[{{2x+2,x≤-1},{(3x)/4,-1<x≤2},{e^(x-2),x>2}}]
Math Input :
Klik di sini

Wolfram Language :
f(x) = Piecewise[{{-x-3,x≤-3},{x+3,-3≤x≤0},{3-2x,0≤x≤3},{Divide[x,2]-Divide[9,2],3≤x}}]
Alternate :
f(x) = Piecewise[{{-x-3,x≤-3},{x+3,-3≤x≤0},{3-2x,0≤x≤3},{x/2-9/2,3≤x}}]
Math Input :
Klik di sini

E. Prakalkulus

Prakalkulus di sini yaitu Limit dan Series (Penjumlahan dan Perkalian).

1. Penjumlahan Berderet

Σ[{a=0;10} 2a+1]

Wolfram Language :
Sum[2a+1,{a,0,10}]
Alternate :
Σ[2a+1,{a,0,10}]
Math Input :
Klik di sini

Σ[{a=0;10} a^2]

Wolfram Language :
Sum[Power[a,2],{a,0,10}]
Alternate :
Sum[a^2,{a,0,10}] or Σ[a^2,{a,0,10}]
Math Input :
Klik di sini

Σ[{x=0;n} x]

Wolfram Language :
Sum[x,{a,0,n}]
Alternate :
Σ[x,{a,0,n}]
Math Input :
Klik di sini

Σ[{a=0;n} x^2]

Wolfram Language :
Sum[Power[x,2],{x,0,n}]
Alternate :
Sum[x^2,{x,0,n}] or Σ[x^2,{x,0,n}]
Math Input :
Klik di sini

Σ[{a=0;n} a^x]

Wolfram Language :
Sum[Power[a,x],{x,0,n}]
Alternate :
Sum[a^x,{x,0,n}] or Σ[a^x,{x,0,n}]
Math Input :
Klik di sini

Σ[{k=1;∞} 1/k^2]

Wolfram Language :
Sum[Divide[1,Power[k,2]],{k,1,∞}]
Alternate :
Sum[1/k^2,{k,1,∞}] or Σ[1/k^2,{k,1,infinity}]
Math Input :
Klik di sini

Σ[{k=0;∞} n^k/k!]

Wolfram Language :
Sum[Divide[Power[n,k],k!],{k,0,∞}]
Alternate :
Sum[n^k/k!,{k,0,∞}] or Σ[n^k/k!,{k,0,infinity}]
Math Input :
Klik di sini

Σ[{k=0;∞} (-1)^k/(2k+1)^2]

Wolfram Language :
Sum[Divide[Power[-1,k],Power[2k+1,2]],{k,0,∞}]
Alternate :
Sum[(-1)^k/(2k+1)^2,{k,0,∞}] or Σ[(-1)^k/(2k+1)^2,{k,0,infinity}]
Math Input :
Klik di sini

Σ[{k=0;∞} (-1)^k/((k+1)(k+2))]

Wolfram Language :
Sum[Divide[Power[-1,k],(k+1)(k+2)],{k,0,∞}]
Alternate :
Sum[(-1)^k/((k+1)(k+2)),{k,0,∞}] or Σ[(-1)^k/((k+1)(k+2)),{k,0,infinity}]
Math Input :
Klik di sini

Σ[{k=0;∞} ((-1)^k*3^(2k))/(2k*(2k)!)]

Wolfram Language :
Sum[Divide[Power[-1,k]*Power[3,2k],2k*(2k)!],{k,0,∞}]
Alternate :
Sum[((-1)^k*3^(2k))/(2k*(2k)!),{k,0,∞}] or Σ[((-1)^k*3^(2k))/(2k*(2k)!),{k,0,infinity}]
Math Input :
Klik di sini

2. Perkalian Berderet

Π[{a=1;10} a+1]

Wolfram Language :
Product[a+1,{a,1,10}]
Alternate :
Π[a+1,{a,1,10}]
Math Input :
Klik di sini

Π[{a=1;n} a^2]

Wolfram Language :
Product[Power[a,2],{a,1,n}]
Alternate :
Product[a^2,{a,1,n}] or Π[a^2,{a,1,n}]
Math Input :
Klik di sini

Π[{x=1;4} (x+1)/x]

Wolfram Language :
Product[Divide[(x+1),x],{x,1,4}]
Alternate :
Product[(x+1)/x,{x,1,4}] or Π[(x+1)/x,{x,1,4}]
Math Input :
Klik di sini

Π[{k=2;∞} (k^2-1)/(k^2+1)]

Wolfram Language :
Product[(Power[k,2]-1)/(Power[k,2]+1),{k,2,∞}]
Alternate :
Product[(k^2-1)/(k^2+1),{k,2,∞}] or Π[(k^2-1)/(k^2+1),{k,2,infinity}]
Math Input :
Klik di sini

Π[{k=2;∞} (1-1/k^2)]

Wolfram Language :
Product[(1-Divide[1,Power[k,2]]),{k,2,∞}]
Alternate :
Product[(1-1/k^2),{k,2,∞}] or Π[(1-1/k^2),{k,2,infinity}]
Math Input :
Klik di sini

Π[{k=1;∞} (1-3^(-k))/(1+3^(-k))]

Wolfram Language :
Product[(1-Power[3,-k])/(1+Power[3,-k]),{k,1,∞}]
Alternate :
Product[(1-3^(-k))/(1+3^(-k)),{k,1,∞}] or Π[(1-3^(-k))/(1+3^(-k)),{k,1,infinity}]
Math Input :
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Π[{q=1;k} (n-q+1)/q]

Wolfram Language :
Product[Divide[n-q+1,q],{q,1,k}]
Alternate :
Product[(n-q+1)/q,{q,1,k}] or Π[(n-q+1)/q,{q,1,k}]
Math Input :
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Π[{k=1;∞} 2/(1+5^(1/(2^k)))]

Wolfram Language :
Product[Divide[2,1+Power[5,Divide[1,Power[2,k]]]],{k,1,∞}]
Alternate :
Product[2/(1+5^(1/(2^k))),{k,1,∞}] or Π[2/(1+5^(1/(2^k))),{k,1,infinity}]
Math Input :
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Π[{k=1;∞} (1+3/k)^(-1)*e^(3/k)]

Wolfram Language :
Product[Power[1+Divide[3,k],-1]*Power[e,Divide[3,k]],{k,1,∞}]
Alternate :
Product[(1+3/k)^(-1)*e^(3/k),{k,1,∞}] or Π[(1+3/k)^(-1)*e^(3/k),{k,1,infinity}]
Math Input :
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https://en.wikipedia.org/wiki/Infinite_product

https://mathworld.wolfram.com/InfiniteProduct.html

https://medium.com/mathadam/how-to-use-%CF%80-product-notation-ae4a4c257471

3. Limit

  

lim(x→1)[3x-1]

Wolfram Language :
Limit[3x-1,x->1]
Alternate :
Limit[3x-1,x->1] or Limit(3x-1,x->1) or Lim(3x-1,x->1)
Math Input :
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lim(x→2)[2x^2+5]

Wolfram Language :
Limit[2Power[x,2]+5,x->2]
Alternate :
Limit[2x^2+5,x->2] or Limit(2x^2+5,x->2) or Lim(2x^2+5,x->2)
Math Input :
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lim(x→-1)[(x^2-2x+1)/(x+2)]

Wolfram Language :
Limit[Divide[Power[x,2]-2x+1,x+2],x->-1]
Alternate :
Limit[(x^2-2x+1)/(x+2),x->-1] or Limit((x^2-2x+1)/(x+2),x->-1) or Lim((x^2-2x+1)/(x+2),x->-1)
Math Input :
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lim(x→2)[(x^2-4)/(x-2)]

Wolfram Language :
Limit[Divide[Power[x,2]-4,x-2],x->2]
Alternate :
Limit[(x^2-4)/(x-2),x->2] or Limit((x^2-4)/(x-2),x->2) or Lim((x^2-4)/(x-2),x->2)
Math Input :
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lim(x→1)[(x^2+4x-5)/(x-1)]

Wolfram Language :
Limit[Divide[Power[x,2]+4x-5,x-1],x->1]
Alternate :
Limit[(x^2+4x-5)/(x-1),x->1] or Limit((x^2+4x-5)/(x-1),x->1) or Lim((x^2+4x-5)/(x-1),x->1)
Math Input :
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lim(x→2)[(x-2)/(sqrt(x)+sqrt(2))]

Wolfram Language :
Limit[Divide[x-2,Sqrt[x]+Sqrt[2]],x->2]
Alternate :
Limit[(x-2)/(sqrt(x)+sqrt(2)),x->2] or Limit((x-2)/(sqrt(x)+sqrt(2)),x->2) or Lim((x-2)/(√x+√2),x->2)
Math Input :
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lim(x→2)[(x^2-3x)/(x^3+2x^2-15x)]

Wolfram Language :
Limit[Divide[Power[x,2]-3x,Power[x,3]+2Power[x,2]-15x],x->2]
Alternate :
Limit[(x^2-3x)/(x^3+2x^2-15x),x->2] or Limit((x^2-3x)/(x^3+2x^2-15x),x->2) or Lim((x^2-3x)/(x^3+2x^2-15x),x->2)
Math Input :
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lim(x→∞)[(4x^2-6x+1)/(3x^2+7x-1)]

Wolfram Language :
Limit[Divide[4Power[x,2]-6x+1,3Power[x,2]+7x-1],x->∞]
Alternate :
Limit[(4x^2-6x+1)/(3x^2+7x-1),x->∞] or Limit((x^2-3x)/(x^3+2x^2-15x),x->infinity) or Lim((x^2-3x)/(x^3+2x^2-15x),x->∞)
Math Input :
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lim(x→∞)[(3x^3-5x^2+2x-4)/(5x^3+x^2-6x+2)]

Wolfram Language :
Limit[Divide[3Power[x,3]-5Power[x,2]+2x-4,5Power[x,3]+Power[x,2]-6x+2],x->∞]
Alternate :
Limit[(3x^3-5x^2+2x-4)/(5x^3+x^2-6x+2),x->∞] or Limit((3x^3-5x^2+2x-4)/(5x^3+x^2-6x+2),x->infinity) or Lim((3x^3-5x^2+2x-4)/(5x^3+x^2-6x+2),x->∞)
Math Input :
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lim(x→∞)[sqrt(x^4-2x^2+3x)/(2x^2-x+1)]

Wolfram Language :
Limit[Divide[Sqrt[Power[x,4]-2Power[x,2]+3x],2Power[x,2]-x+1],x->∞]
Alternate :
Limit[sqrt(x^4-2x^2+3x)/(2x^2-x+1),x->∞] or Limit(sqrt(x^4-2x^2+3x)/(2x^2-x+1),x->infinity) or Lim(√(x^4-2x^2+3x)/(2x^2-x+1),x->∞)
Math Input :
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lim(x→∞)[sqrt(4x^2+3x-1)-sqrt(4x^2-x+2)]

Wolfram Language :
Limit[Sqrt[4Power[x,2]+3x-1]-Sqrt[4Power[x,2]-x+2],x->∞]
Alternate :
Limit[sqrt(4x^2+3x-1)-sqrt(4x^2-x+2),x->∞] or Limit(sqrt(4x^2+3x-1)-sqrt(4x^2-x+2),x->infinity) or Lim(√(4x^2+3x-1)-√(4x^2-x+2),x->∞)
Math Input :
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lim(x→∞)[(x+3)-sqrt(x^2-4x)]

Wolfram Language :
Limit[(x+3)-Sqrt[Power[x,2]-4x],x->∞]
Alternate :
Limit[(x+3)-sqrt(x^2-4x),x->∞] or Limit((x+3)-sqrt(x^2-4x),x->infinity) or Lim((x+3)-√(x^2-4x),x->∞)
Math Input :
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lim(x→∞)[sqrt(3x^2-8x)-sqrt(x^2+1)-sqrt(x^2+x)]

Wolfram Language :
Limit[Sqrt[3Power[x,2]-8x]-Sqrt[Power[x,2]+1]-Sqrt[Power[x,2]+x],x->∞]
Alternate :
Limit[sqrt(3x^2-8x)-sqrt(x^2+1)-sqrt(x^2+x),x->∞] or Limit(sqrt(3x^2-8x)-sqrt(x^2+1)-sqrt(x^2+x),x->infinity) or Lim(√(3x^2-8x)-√(x^2+1)-√(x^2+x),x->∞)
Math Input :
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lim(x→∞)[cbrt(2x^3+5x^2+x-7)-cbrt(2x^3-3x^2-4x+1)]

Wolfram Language :
Limit[(Cbrt[2Power[x,3]+5Power[x,2]+x-7]-Cbrt[2Power[x,3]-3Power[x,2]-4x+1]),x->∞]
Alternate :
Limit[cbrt(2x^3+5x^2+x-7)-cbrt(2x^3-3x^2-4x+1),x->∞] or Limit(cbrt(2x^3+5x^2+x-7)-cbrt(2x^3-3x^2-4x+1),x->infinity) or Lim(cbrt(2x^3+5x^2+x-7)-cbrt(2x^3-3x^2-4x+1),x->∞)
Math Input :
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lim(x→4)[(4-x)/(x-sqrt(6x-8))]

Wolfram Language :
Limit[Divide[4-x,x-Sqrt[6x-8]],x->4]
Alternate :
Limit[(4-x)/(x-sqrt(6x-8)),x->4] or Limit((4-x)/(x-sqrt(6x-8)),x->4) or Lim((4-x)/(x-√(6x-8)),x->4)
Math Input :
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lim(x→0+)[x/abs(x)]

Wolfram Language :
Limit[x/Abs[x],x->0,Direction->-1]
Alternate :
Limit[x/abs(x),x->0,direction->-1] or Limit(x/abs(x),x->0,direction->-1) or Lim(x/|x|,x->0,direction->-1)
Math Input :
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lim(x→1-)[(x-1)/abs(x-1)]

Wolfram Language :
Limit[(x-1)/Abs[x-1],x->1,Direction->1]
Alternate :
Limit[(x-1)/abs(x-1),x->1,direction->1] or Limit((x-1)/abs(x-1),x->1,direction->1) or Lim((x-1)/|x-1|,x->1,direction->1)
Math Input :
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lim(x→1)[(x^2-2x+1)^(2x-2)]

Wolfram Language :
Limit[Power[(Power[x,2]-2x+1),2x-2],x->1]
Alternate :
Limit[(x^2-2x+1)^(2x-2),x->1] or Limit((x^2-2x+1)^(2x-2),x->1) or Lim((x^2-2x+1)^(2x-2),x->1)
Math Input :
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lim(x→π/2)[cos⁡(x)]

Wolfram Language :
Limit[Cos⁡[x],x->Divide[π,2]]
Alternate :
Limit[cos⁡(x),x->π/2] or Limit(cos⁡(x),x->pi/2) or Lim(cos⁡(x),x->π/2)
Math Input :
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lim(x→0)[sin⁡(3x)/2x]

Wolfram Language :
Limit[Divide[Sin⁡[3x],2x],x->0]
Alternate :
Limit[sin⁡(3x)/(2x),x->0] or Limit(sin⁡(3x)/(2x),x->0) or Lim(sin⁡(3x)/(2x),x->0)
Math Input :
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lim(x→0)[(sin⁡(x)-x)/x^3]

Wolfram Language :
Limit[Divide[Sin⁡[x]-x,Power[x,3]],x->0]
Alternate :
Limit[(sin⁡(x)-x)/x^3,x->0] or Limit((sin⁡(x)-x)/x^3,x->0) or Lim((sin⁡(x)-x)/x^3,x->0)
Math Input :
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lim(x→4)[sin⁡(x-2)/(x^2-4x+4)]

Wolfram Language :
Limit[Divide[Sin⁡[x-2],Power[x,2]-4x+4],x->4]
Alternate :
Limit[sin⁡(x-2)/(x^2-4x+4),x->4] or Limit(sin⁡(x-2)/(x^2-4x+4),x->4) or Lim(sin⁡(x-2)/(x^2-4x+4),x->4)
Math Input :
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lim(x→π/4)[sin⁡(x-2)/(x^2-4x+4)]

Wolfram Language :
Limit[Divide[1-Sin⁡[x],x-Divide[π,2]],x->Divide[π,4]]
Alternate :
Limit[(1-sin⁡(x))/(x-π/2),x->π/4] or Limit((1-sin⁡(x))/(x-pi/2),x->pi/4) or Lim((1-sin⁡(x))/(x-π/2),x->π/4)
Math Input :
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lim(x→π/4)[(1-sin⁡(x))/(x-π/2)]

Wolfram Language :
Limit[Divide[6(x-π)Power[Cos[x],2],π(π-2x)Tan[x-Divide[π,2]]],x->Divide[π,4]]
Alternate :
Limit[(6(x-π)cos^2(x))/(π(π-2x)tan⁡(x-π/2)),x->π/4] or Limit((6(x-pi)cos^2(x))/(pi(pi-2x)tan⁡(x-pi/2)),x->pi/4) or Lim((6(x-π)cos^2(x))/(π(π-2x)tan⁡(x-π/2)),x->π/4)
Math Input :
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lim(x→∞)[(5^x+3)/(5^(x+2)-7)]

Wolfram Language :
Limit[Divide[Power[5,x]+3,Power[5,x+2]-7],x->∞]
Alternate :
Limit[(5^x+3)/(5^(x+2)-7),x->∞] or Limit((5^x+3)/(5^(x+2)-7),x->infinity) or Lim((5^x+3)/(5^(x+2)-7),x->∞)
Math Input :
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lim(x→∞)[(2^(x+1)-3^(x-2)+4^(x+1))/(2^(x-1)-3^(x+1)+4^(x-1))]

Wolfram Language :
Limit[Divide[Power[2,x+1]-Power[3,x-2]+Power[4,x+1],Power[2,x-1]-Power[3,x+1]+Power[4,x-1]],x->∞]
Alternate :
Limit[(2^(x+1)-3^(x-2)+4^(x+1))/(2^(x-1)-3^(x+1)+4^(x-1)),x->∞] or Limit((2^(x+1)-3^(x-2)+4^(x+1))/(2^(x-1)-3^(x+1)+4^(x-1)),x->infinity) or Lim((2^(x+1)-3^(x-2)+4^(x+1))/(2^(x-1)-3^(x+1)+4^(x-1)),x->∞)
Math Input :
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lim(k→∞)[(1+1/k)^k]

Wolfram Language :
Limit[Power[1+1/k,k],k->∞]
Alternate :
Limit[(1+1/k)^k,k->∞] or Limit((1+1/k)^k,k->infinity) or Lim((1+1/k)^k,k->∞)
Math Input :
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lim(k→∞)[(1+1/k)^k]

Wolfram Language :
Limit[Power[Divide[(Power[2,k]+Power[5,k]),2],Divide[1,k]],k->∞]
Alternate :
Limit[((2^k+5^k)/2)^(1/k),k->∞] or Limit(((2^k+5^k)/2)^(1/k),k->infinity) or Lim(((2^k+5^k)/2)^(1/k),k->∞)
Math Input :
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lim(n→∞)[(n!/n^n)^(1/n)]

Wolfram Language :
Limit[Power[(Divide[n!,Power[n,n]]),Divide[1,n]],n->∞]
Alternate :
Limit[(n!/n^n)^(1/n),n->∞] or Limit((n!/n^n)^(1/n),n->infinity) or Lim((n!/n^n)^(1/n),n->∞)
Math Input :
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lim(x→∞)[ln(x^(5x^x)*x^3x)/ln(x^(2x^x)*x^4x)]

Wolfram Language :
Limit[Divide[Log[x^(5x^x)*x^3x],Log[x^(2x^x)*x^4x]],x->∞]
Alternate :
Limit[log(x^(5x^x)*x^3x)/log(x^(2x^x)*x^4x),x->∞] or Limit(log(x^(5x^x)*x^3x)/log(x^(2x^x)*x^4x),x->infinity) or Lim(log(x^(5x^x)*x^3x)/log(x^(2x^x)*x^4x),x->∞)
Math Input :
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lim(n→∞)[n*sin⁡(2/n*abs(arcsin⁡(1-1/n^2)))]

Wolfram Language :
Limit[n*Sin⁡[Divide[2,n]*Abs[ArcSin⁡[1-Divide[1,Power[n,2]]]]],n->∞]
Alternate :
Limit[n*sin⁡(2/n*abs(arcsin⁡(1-1/n^2))),n->∞] or Limit(n*sin⁡(2/n*abs(arcsin⁡(1-1/n^2))),n->infinity) or Lim(n*sin⁡(2/n*|arcsin⁡(1-1/n^2)|),n->∞)
Math Input :
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4. Limit 2 Dimensi

lim((x,y)→(-1,2))[(x+y)/(x-y)]

Wolfram Language :
Limit[Divide[x+y,x-y],(x,y)->(-1,2)]
Alternate :
Limit[(x+y)/(x-y),(x,y)->(-1,2)] or Limit((x+y)/(x-y),(x,y)->(-1,2)) or Lim((x+y)/(x-y),(x,y)->(-1,2))
Math Input :
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lim((x,y)→(0,0))[(x+y)/(x-y)]

Wolfram Language :
Limit[Divide[2xy,Power[x,2]+2Power[y,2]],(x,y)->(0,0)]
Alternate :
Limit[(2xy)/(x^2+2y^2),(x,y)->(0,0)] or Limit((2xy)/(x^2+2y^2),(x,y)->(0,0)) or Lim((2xy)/(x^2+2y^2),(x,y)->(0,0))
Math Input :
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lim((x,y)→(1,1))[(x^2-2xy+y^2)/(x^2-y^2)]

Wolfram Language :
Limit[Divide[x^2-2xy+y^2,x^2-y^2],(x,y)->(1,1)]
Alternate :
Limit[(x^2-2xy+y^2)/(x^2-y^2),(x,y)->(1,1)] or Limit((x^2-2xy+y^2)/(x^2-y^2),(x,y)->(1,1)) or Lim((x^2-2xy+y^2)/(x^2-y^2),(x,y)->(1,1))
Math Input :
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lim((x,y)→(0,0))[(xy)/sqrt(x^2+y^2)]

Wolfram Language :
Limit[Divide[xy,Sqrt[Power[x,2]+Power[y,2]]],(x,y)->(0,0)]
Alternate :
Limit[(xy)/sqrt(x^2+y^2),(x,y)->(0,0)] or Limit((xy)/sqrt(x^2+y^2),(x,y)->(0,0)) or Lim((xy)/√(x^2+y^2),(x,y)->(0,0))
Math Input :
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lim((x,y)→(2,4))[sin⁡(x^2-y)/(x^2-y)]

Wolfram Language :
Limit[Divide[Sin⁡[Power[x,2]-y],Power[x,2]-y],(x,y)->(2,4)]
Alternate :
Limit[sin⁡(x^2-y)/(x^2-y),(x,y)->(2,4)] or Limit(sin⁡(x^2-y)/(x^2-y),(x,y)->(2,4)) or Lim(sin⁡(x^2-y)/(x^2-y),(x,y)->(2,4))
Math Input :
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lim((x,y)→(1,1))[(2y^4cos^2⁡(x))/(x^4+y^4)]

Wolfram Language :
Limit[Divide[2Power[y,4]Power[Cos[x],2],Power[x,4]+Power[y,4]],(x,y)->(0,0)]
Alternate :
Limit[(2y^4cos^2⁡(x))/(x^4+y^4),(x,y)->(0,0)] or Limit((2y^4cos^2⁡(x))/(x^4+y^4),(x,y)->(0,0)) or Lim((2y^4cos^2⁡(x))/(x^4+y^4),(x,y)->(0,0))
Math Input :
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lim((x,y)→(1,-1))[(x^2y)/(1+xy^2)]

Wolfram Language :
Limit[Divide[Power[x,2]y,1+xPower[y,2]],(x,y)->(1,-1)]
Alternate :
Limit[(x^2y)/(1+xy^2),(x,y)->(1,-1)] or Limit((x^2y)/(1+xy^2),(x,y)->(1,-1)) or Lim((x^2y)/(1+xy^2),(x,y)->(1,-1))
Math Input :
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lim((x,y)→(1,1))[(x-sqrt(y))/(y-x^2)]

Wolfram Language :
Limit[Divide[x-Sqrt[y],y-Power[x,2]],(x,y)->(1,1)]
Alternate :
Limit[(x-sqrt(y))/(y-x^2),(x,y)->(1,1)] or Limit((x-sqrt(y))/(y-x^2),(x,y)->(1,1)) or Lim((x-√y)/(y-x^2),(x,y)->(1,1))
Math Input :
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lim((x,y)→(1,1))[(sqrt(5x)-sqrt(2y+3))/(5x-2y-3)]

Wolfram Language :
Limit[Divide[Sqrt[5x]-Sqrt[2y+3],5x-2y-3],(x,y)->(1,1)]
Alternate :
Limit[(sqrt(5x)-sqrt(2y+3))/(5x-2y-3),(x,y)->(1,1)] or Limit((sqrt(5x)-sqrt(2y+3))/(5x-2y-3),(x,y)->(1,1)) or Lim((√(5x)-√(2y+3))/(5x-2y-3),(x,y)->(1,1))
Math Input :
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F. Kalkulus

Kalkulus di sini yaitu Integral dan Turunan/Diferensial. Untuk Turunan yaitu Turunan Pertama, Kedua, sampai Turunan ke-n. Sedangkan untuk Integral ada Integral Tentu (Definite Integral) dan Integral Tak Tentu (Indefinite Integral). Juga untuk Integral ada Integral Lipat Dua hingga Lipat ke-n.

1. Turunan (Derivative)

d/dx(2x)

Wolfram Language :
D[2x,x]
Alternate :
d/dx(2x) or "d/dx 2x" or (2x)'
Math Input :
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d/dx(x^2)

Wolfram Language :
D[Power[x,2],x]
Alternate :
D[x^2,x] or d/dx(x^2) or "d/dx x^2" or (x^2)'
Math Input :
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d/dx(x^3-2x+5)

Wolfram Language :
D[Power[x,3]-2x+5,x]
Alternate :
D[x^3-2x+5,x] or d/dx(x^3-2x+5) or "d/dx x^3-2x+5" or (x^3-2x+5)'
Math Input :
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d/dx(sqrt(x^2+4-3))

Wolfram Language :
D[Sqrt[Power[x,2]+4x-3],x]
Alternate :
D[sqrt(x^2+4x-3),x] or d/dx(sqrt(x^2+4x-3)) or "d/dx √(x^2+4x-3)" or (√(x^2+4x-3))'
Math Input :
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d/dx((3x-2)(x^3+2x^2+1))

Wolfram Language :
D[(3x-2)(Power[x,3]+2Power[x,2]+1),x]
Alternate :
D[(3x-2)(x^3+2x^2+1),x] or d/dx((3x-2)(x^3+2x^2+1)) or "d/dx (3x-2)(x^3+2x^2+1)" or ((3x-2)(x^3+2x^2+1))'
Math Input :
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d/dx(2xsqrt(x)+1/sqrt(x))

Wolfram Language :
D[2xSqrt[x]+Divide[1,Sqrt[x]],x]
Alternate :
D[2xsqrt(x)+1/sqrt(x),x] or d/dx(2xsqrt(x)+1/sqrt(x)) or "d/dx 2x√x+1/√x" or (2x√x+1/√x)'
Math Input :
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d/dx((3x+9)/(2-x))

Wolfram Language :
D[Divide[3x+9,2-x],x]
Alternate :
D[(3x+9)/(2-x),x] or d/dx((3x+9)/(2-x)) or "d/dx (3x+9)/(2-x)" or ((3x+9)/(2-x))'
Math Input :
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d/dx(sqrt(x)/(2x+3))

Wolfram Language :
D[Divide[Sqrt[x],2x+3],x]
Alternate :
D[sqrt(x)/(2x+3),x] or d/dx(sqrt(x)/(2x+3)) or "d/dx √x/(2x+3)" or (√x/(2x+3))'
Math Input :
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d/dx((x^2+3xsqrt(x))/sqrt(x))

Wolfram Language :
D[Divide[Power[x,2]+3xSqrt[x],Sqrt[x]],x]
Alternate :
D[(x^2+3xsqrt(x))/sqrt(x),x] or d/dx((x^2+3xsqrt(x))/sqrt(x)) or "d/dx (x^2+3x√x)/√x" or ((x^2+3x√x)/√x)'
Math Input :
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d/dx(5^x)

Wolfram Language :
D[Power[5,x],x]
Alternate :
D[5^x,x] or d/dx(5^x) or "d/dx 5^x" or (5^x)'
Math Input :
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d/dx(4^x+3^(x+2))

Wolfram Language :
D[Power[4,x]+Power[3,x+2],x]
Alternate :
D[4^x+3^(x+2),x] or d/dx(4^x+3^(x+2)) or "d/dx 4^x+3^(x+2)" or (4^x+3^(x+2))'
Math Input :
Klik di sini

d/dx(x^3-2x+5)

Wolfram Language :
D[Sin[x]+Cos[x],x]
Alternate :
D[sin⁡(x)+cos⁡(x),x] or d/dx(sin⁡(x)+cos⁡(x)) or "d/dx sin⁡(x)+cos⁡(x)" or (sin⁡(x)+cos⁡(x))'
Math Input :
Klik di sini

d/dx(x^4sin⁡(x))

Wolfram Language :
D[Power[x,4]Sin⁡[x],x]
Alternate :
D[x^4sin⁡(x),x] or d/dx(x^4sin⁡(x)) or "d/dx x^4sin⁡(x)" or (x^4sin⁡(x))'
Math Input :
Klik di sini

d/dx(tan⁡(x)+cot(x))

Wolfram Language :
D[Tan⁡[x]+Cot[x],x]
Alternate :
D[tan⁡(x)+cot(x),x] or d/dx(tan⁡(x)+cot(x)) or "d/dx tan⁡(x)+cot(x)" or (tan⁡(x)+cot(x))'
Math Input :
Klik di sini

d/dx(arcsin⁡(x)+arcsec⁡(x))

Wolfram Language :
D[ArcSin[x]+ArcSec[x],x]
Alternate :
D[arcsin⁡(x)+arcsec⁡(x),x] or d/dx(arcsin⁡(x)+arcsec⁡(x)) or "d/dx sin^-1⁡(x)+sec^-1⁡(x)" or (arcsin⁡(x)+arcsec⁡(x))'
Math Input :
Klik di sini

d/dx(arccsc⁡(x)-csc⁡(x))

Wolfram Language :
D[ArcCsc[x]-Csc[x],x]
Alternate :
D[arccsc⁡(x)-csc⁡(x),x] or d/dx(arccsc⁡(x)-csc⁡(x)) or "d/dx csc⁡^-1(x)-csc⁡(x)" or (arccsc⁡(x)-csc⁡(x))'
Math Input :
Klik di sini

d/dx(3sin⁡(6-3x))

Wolfram Language :
D[3Sin⁡[6-3x],x]
Alternate :
D[3sin⁡(6-3x),x] or d/dx(3sin⁡(6-3x)) or "d/dx 3sin⁡(6-3x)" or (3sin⁡(6-3x))'
Math Input :
Klik di sini

d/dx(2cos(x^2-2x))

Wolfram Language :
D[2Cos[Power[x,2]-2x],x]
Alternate :
D[2cos(x^2-2x),x] or d/dx(2cos(x^2-2x)) or "d/dx 2cos(x^2-2x)" or (2cos(x^2-2x))'
Math Input :
Klik di sini

d/dx(sin⁡(x-1)/sin⁡(x+1))

Wolfram Language :
D[Divide[Sin[x-1],Sin⁡[x+1]],x]
Alternate :
D[sin⁡(x-1)/sin⁡(x+1),x] or d/dx(sin⁡(x-1)/sin⁡(x+1)) or "d/dx sin⁡(x-1)/sin⁡(x+1)" or (sin⁡(x-1)/sin⁡(x+1))'
Math Input :
Klik di sini

d/dx(cos⁡(x)sin⁡(2x))

Wolfram Language :
D[Cos⁡[x]Sin⁡[2x],x]
Alternate :
D[cos⁡(x)sin⁡(2x),x] or d/dx(cos⁡(x)sin⁡(2x)) or "d/dx cos⁡(x)*sin⁡(2x)" or (cos⁡(x)*sin⁡(2x))'
Math Input :
Klik di sini

d/dx(sin^4⁡(3x^2-4x+1))

Wolfram Language :
D[Power[Sin[3x^2-4x+1],4],x]
Alternate :
D[sin^4⁡(3x^2-4x+1),x] or d/dx(sin^4⁡(3x^2-4x+1)) or "d/dx sin^4⁡(3x^2-4x+1)" or (sin^4⁡(3x^2-4x+1))'
Math Input :
Klik di sini

d/dx(sqrt(cos⁡(4x)))

Wolfram Language :
D[Sqrt[Cos⁡[4x]],x]
Alternate :
D[sqrt(cos⁡(4x)),x] or d/dx(sqrt(cos⁡(4x))) or "d/dx √(cos⁡(4x))" or (√(cos⁡(4x)))'
Math Input :
Klik di sini

2. Turunan Kedua (Second-Order Derivative)

d^2/dx^2(x^4+5x^3)

Wolfram Language :
D[Power[x,4]+5Power[x,3],{x,2}]
Alternate :
D[x^4+5x^3,{x,2}] or d^2/dx^2(x^4+5x^3) or "d^2/dx^2 x^4+5x^3" or (x^4+5x^3)''
Math Input :
Klik di sini

d^2/dx^2((3x+9)/(x-2))

Wolfram Language :
D[Divide[3x+9,x-2],{x,2}]
Alternate :
D[(3x+9)/(x-2),{x,2}] or d^2/dx^2((3x+9)/(x-2)) or "d^2/dx^2 (3x+9)/(x-2)" or ((3x+9)/(x-2))''
Math Input :
Klik di sini

d^2/dx^2(sqrt(x)/(2x+3))

Wolfram Language :
D[Divide[Sqrt[x],2x+3],{x,2}]
Alternate :
D[sqrt(x)/(2x+3),{x,2}] or d^2/dx^2(sqrt(x)/(2x+3)) or "d^2/dx^2 sqrt(x)/(2x+3)" or (sqrt(x)/(2x+3))''
Math Input :
Klik di sini

d^2/dx^2(sin⁡(x)+cos⁡(x))

Wolfram Language :
D[Sin[x]+Cos[x],{x,2}]
Alternate :
D[sin⁡(x)+cos⁡(x),{x,2}] or d^2/dx^2(sin⁡(x)+cos⁡(x)) or "d^2/dx^2 sin⁡(x)+cos⁡(x)" or (sin⁡(x)+cos⁡(x))''
Math Input :
Klik di sini

d^2/dx^2(e^x^n)

Wolfram Language :
D[Power[e,Power[x,n]],{x,2}]
Alternate :
D[e^x^n,{x,2}] or d^2/dx^2(e^x^n) or "d^2/dx^2 e^x^n" or (e^x^n)''
Math Input :
Klik di sini

d^2/dx^2(x ln(x))

Wolfram Language :
D[x Log[x],{x,2}]
Alternate :
D[xlog(x),{x,2}] or d^2/dx^2(xlog(x)) or "d^2/dx^2 xlog(x)" or (xlog(x))''
Math Input :
Klik di sini

3. Turunan Parsial (Partial Derivative)

∂/∂x(x^3-2y^2)

Wolfram Language :
Partial[Power[x,3]-2Power[y,2],x]
Alternate :
Partial[x^3-2y^2,x] or ∂/∂x(x^3-2y^2)
Math Input :
Klik di sini

∂/∂x(x^2 y^2)

Wolfram Language :
Partial[Power[x,2]Power[y,2],x]
Alternate :
Partial[x^2 y^2,x] or ∂/∂x(x^2 y^2)
Math Input :
Klik di sini

∂/∂x(sin(x^3-3y^2))

Wolfram Language :
Partial[Sin[Power[x,3]-3Power[y,2]],x]
Alternate :
Partial[sin(x^3-3y^2),x] or ∂/∂x(sin(x^3-3y^2))
Math Input :
Klik di sini

∂/∂y(cos(x^4+y^3))

Wolfram Language :
Partial[Cos[Power[x,4]-Power[y,3]],y]
Alternate :
Partial[cos(x^4+y^3),y] or ∂/∂y(cos(x^4+y^3))
Math Input :
Klik di sini

∂/∂t(te^(k/t))

Wolfram Language :
Partial[t Power[e,Divide[k,t]],t]
Alternate :
Partial[te^(k/t),t] or ∂/∂t(te^(k/t))
Math Input :
Klik di sini

∂/∂x(sqrt(x^2+y^2))

Wolfram Language :
Partial[Sqrt[Power[x,2]+Power[y,2]],x]
Alternate :
Partial[sqrt(x^2+y^2),x] or ∂/∂x(sqrt(x^2+y^2)) or ∂/∂x(√(x^2+y^2))
Math Input :
Klik di sini

∂/∂y((2x+y)^6)

Wolfram Language :
Partial[Power[(2x+y),6],y]
Alternate :
Partial[(2x+y)^6,y] or ∂/∂y((2x+y)^6)
Math Input :
Klik di sini

∂/∂y((x+4y)/(x-4y))

Wolfram Language :
Partial[Divide[(x+4y),(x-4y)],y]
Alternate :
Partial[(x+4y)/(x-4y),y] or ∂/∂y((x+4y)/(x-4y))
Math Input :
Klik di sini

∂/∂x(e^(-2x)sin⁡(4y))

Wolfram Language :
Partial[Power[e,-2x]Sin[4y],x]
Alternate :
Partial[e^(-2x)sin⁡(4y),x] or ∂/∂x(e^(-2x)sin⁡(4y))
Math Input :
Klik di sini

https://activecalculus.org/multi/S-10-2-First-Order-Partial-Derivatives.html

4. Turunan Parsial Kedua (Second-Order Partial Derivative)

∂^2/∂x^2(x^3+4x^2y^2+y^3)

Wolfram Language :
Partial[Power[x,3]+4Power[x,2]Power[y,3]+Power[y,3],{x,2}]
Alternate :
Partial[x^3+4x^2y^2+y^3,{x,2}] or ∂^2/∂x^2(x^3+4x^2y^2+y^3)
Math Input :
Klik di sini

∂^2/∂y^2(4x^3y^2+8x^2y^3)

Wolfram Language :
Partial[4Power[x,3]Power[y,2]+8Power[x,2]Power[y,3],{y,2}]
Alternate :
Partial[4x^3y^2+8x^2y^3,{y,2}] or ∂^2/∂y^2(4x^3y^2+8x^2y^3)
Math Input :
Klik di sini

∂^2/∂x^2(3sin⁡(2x+y)-4cos⁡(x-y))

Wolfram Language :
Partial[3Sin[2x+y]-4Cos[x-y],{x,2}]
Alternate :
Partial[3sin⁡(2x+y)-4cos⁡(x-y),{x,2}] or ∂^2/∂x^2(3sin⁡(2x+y)-4cos⁡(x-y))
Math Input :
Klik di sini

∂^2/∂y^2(xye^(2xy))

Wolfram Language :
Partial[xy Power[e,2xy],{y,2}]
Alternate :
Partial[xye^(2xy),{y,2}] or ∂^2/∂y^2(xye^(2xy))
Math Input :
Klik di sini

https://activecalculus.org/multi/S-10-3-Second-Order-Partial-Derivatives.html

5. Integral Tak Tentu (Indefinite Integral)

Integrate[x^2 dx]

Wolfram Language :
Integrate[Power[x,2],x]
Alternate :
Integrate[x^2,x] or Integrate[x^2] or "integrate x^2 dx"
Math Input :
Klik di sini

Integrate[2x^3 dx]

Wolfram Language :
Integrate[2Power[x,3],x]
Alternate :
Integrate[2x^3,x] or Integrate[2x^3] or "integrate 2x^3 dx"
Math Input :
Klik di sini

Integrate[1/2x^3-3x^2+2x dx]

Wolfram Language :
Integrate[Divide[1,2]Power[x,3]-3Power[x,2]+2x,x]
Alternate :
Integrate[1/2x^3-3x^2+2x,x] or Integrate[1/2x^3-3x^2+2x] or "integrate 1/2x^3-3x^2+2x dx"
Math Input :
Klik di sini

Integrate[x^4+7x^3+2x-1 dx]

Wolfram Language :
Integrate[Power[x,4]+7Power[x,3]+2x-1,x]
Alternate :
Integrate[x^4+7x^3+2x-1,x] or Integrate[x^4+7x^3+2x-1] or "integrate x^4+7x^3+2x-1 dx"
Math Input :
Klik di sini

Integrate[2^x dx]

Wolfram Language :
Integrate[Power[2,x],x]
Alternate :
Integrate[2^x,x] or Integrate[2^x] or "integrate 2^x dx"
Math Input :
Klik di sini

Integrate[1/sqrt(x) dx]

Wolfram Language :
Integrate[1/Sqrt[x],x]
Alternate :
Integrate[1/sqrt(x),x] or Integrate[1/√x] or "integrate 1/sqrt(x) dx"
Math Input :
Klik di sini

Integrate[(8x+15)^10 dx]

Wolfram Language :
Integrate[Power[8x+15,10],x]
Alternate :
Integrate[(8x+15)^10,x] or Integrate[(8x+15)^10] or "integrate (8x+15)^10 dx"
Math Input :
Klik di sini

Integrate[(3t^(-4)(2+4t^(-3)))^(-7) dt]

Wolfram Language :
Integrate[3Power[t,-4]Power[2+4Power[t,-3],-7],t]
Alternate :
Integrate[3t^(-4) (2+4t^(-3))^(-7),t] or Integrate[3t^(-4) (2+4t^(-3))^(-7)] or "integrate 3t^(-4) (2+4t^(-3))^(-7) dt"
Math Input :
Klik di sini

Integrate[6x(3x-1)^(-1/3) dx]

Wolfram Language :
Integrate[6x Power[3x-1,-Divide[1,3]],x]
Alternate :
Integrate[6x(3x-1)^(-1/3),x] or Integrate[6x(3x-1)^(-1/3)] or "integrate 6x(3x-1)^(-1/3) dx"
Math Input :
Klik di sini

Integrate[(3x+1)sqrt(3x^2+2x-4) dx]

Wolfram Language :
Integrate[(3x+1)Sqrt[3Power[x,2]+2x-4],x]
Alternate :
Integrate[(3x+1)sqrt(3x^2+2x-4),x] or Integrate[(3x+1)√(3x^2+2x-4)] or "integrate (3x+1)sqrt(3x^2+2x-4) dx"
Math Input :
Klik di sini

Integrate[(3x)/(x^2+7x-8) dx]

Wolfram Language :
Integrate[Divide[3x,Power[x,2]+7x-8],x]
Alternate :
Integrate[(3x)/(x^2+7x-8),x] or Integrate[(3x)/(x^2+7x-8)] or "integrate (3x)/(x^2+7x-8) dx"
Math Input :
Klik di sini

Integrate[(2x+1)/(x+5)^3 dx]

Wolfram Language :
Integrate[Divide[2x+1,Power[x+5,3]],x]
Alternate :
Integrate[(2x+1)/(x+5)^3,x] or Integrate[(2x+1)/(x+5)^3] or "integrate (2x+1)/(x+5)^3 dx"
Math Input :
Klik di sini

Integrate[(x^2-1)/(x^3sqrt(2x^4-x^2+3)) dx]

Wolfram Language :
Integrate[Divide[Power[x,2]-1,Power[x,3]Sqrt[2Power[x,4]-Power[x,2]+3]],x]
Alternate :
Integrate[(x^2-1)/(x^3sqrt(2x^4-x^2+3)),x] or Integrate[(x^2-1)/(x^3√(2x^4-x^2+3))] or "integrate (x^2-1)/(x^3sqrt(2x^4-x^2+3)) dx"
Math Input :
Klik di sini

Integrate[sin⁡(x)+cos⁡(x) dx]

Wolfram Language :
Integrate[Sin⁡[x]+Cos⁡[x],x]
Alternate :
Integrate[sin⁡(x)+cos⁡(x),x] or Integrate[sin⁡(x)+cos⁡(x)] or "integrate sin⁡(x)+cos⁡(x) dx"
Math Input :
Klik di sini

Integrate[e^x cos⁡(x) dx]

Wolfram Language :
Integrate[Power[e,x]Cos⁡[x],x]
Alternate :
Integrate[e^x cos⁡(x),x] or Integrate[e^x cos⁡(x)] or "integrate e^x cos⁡(x) dx"
Math Input :
Klik di sini

Integrate[cos^3(x)sin(x) dx]

Wolfram Language :
Integrate[Power[cos[x],3]Sin[x],x]
Alternate :
Integrate[cos^3(x)sin(x),x] or Integrate[cos^3(x)sin(x)] or "integrate cos^3(x)sin(x) dx"
Math Input :
Klik di sini

Integrate[(2xsin(2x))/(2x-sin(2x))^2 dx]

Wolfram Language :
Integrate[Divide[2xSin[2x],Power[2x-Sin[2x],2]],x]
Alternate :
Integrate[(2xsin(2x))/(2x-sin(2x))^2,x] or Integrate[(2xsin(2x))/(2x-sin(2x))^2] or "integrate (2xsin(2x))/(2x-sin(2x))^2 dx"
Math Input :
Klik di sini

Integrate[x^2ln(2x) dx]

Wolfram Language :
Integrate[Power[x,2]Log[2x],x]
Alternate :
Integrate[x^2log(2x),x] or Integrate[x^2log(2x)] or "integrate x^2log(2x) dx"
Math Input :
Klik di sini

Integrate[1/(1+x^2) dx]

Wolfram Language :
Integrate[Divide[1,1+Power[x,2]],x]
Alternate :
Integrate[1/(1+x^2),x] or Integrate[1/(1+x^2)] or "integrate 1/(1+x^2) dx"
Math Input :
Klik di sini

Integrate[(e^(2x))/(1+e^(2x)) dx]

Wolfram Language :
Integrate[Divide[Power[e,2x],1+Power[e,2x]],x]
Alternate :
Integrate[(e^(2x))/(1+e^(2x)),x] or Integrate[(e^(2x))/(1+e^(2x))] or "integrate (e^(2x))/(1+e^(2x)) dx"
Math Input :
Klik di sini

6. Integral Ganda Tak Tentu (Indefinite Double Integral)

Integrate[x^2 dx^2] = Integrate[x^2 dx dx]

Wolfram Language :
Integrate[Power[x,2],x,x]
Alternate :
Integrate[x^2,x,x] or "integrate x^2 dx dx"
Math Input :
Klik di sini

Integrate[1/x dx^2] = Integrate[1/x dx dx]

Wolfram Language :
Integrate[Divide[1,x],x,x]
Alternate :
Integrate[1/x,x,x] or "integrate 1/x dx dx"
Math Input :
Klik di sini

Integrate[x^2+y^2 dx dy]

Wolfram Language :
Integrate[Power[x,2]+Power[y,2],x,y]
Alternate :
Integrate[x^2+y^2,x,y] or "integrate x^2+y^2 dx dy"
Math Input :
Klik di sini

Integrate[xsin⁡(y) dx dy]

Wolfram Language :
Integrate[xSin[y],x,y]
Alternate :
Integrate[xsin⁡(y),x,y] or "integrate xsin⁡(y) dx dy"
Math Input :
Klik di sini

Integrate[(3x+8)^7(2y-5)^6 dx dy]

Wolfram Language :
Integrate[Cos[xy],x,y]
Alternate :
Integrate[cos(xy),x,y] or "integrate cos(xy) dx dy"
Math Input :
Klik di sini

Integrate[(3x+8)^7(2y-5)^6 dx dy]

Wolfram Language :
Integrate[Power[3x+8,7]Power[2y-5,6],x,y]
Alternate :
Integrate[(3x+8)^7(2y-5)^6,x,y] or "integrate (3x+8)^7(2y-5)^6 dx dy"
Math Input :
Klik di sini

7. Integral Rangkap Tiga Tak Tentu (Indefinite Triple Integral)

Integrate[x^2 dx^3] = Integrate[x^2 dx dx dx]

Wolfram Language :
Integrate[2Power[x,2],x,x,x]
Alternate :
Integrate[2x^2,x,x,x] or "integrate 2x^2 dx dx dx"
Math Input :
Klik di sini

Integrate[x+y+z dx dy dz]

Wolfram Language :
Integrate[x+y+z,x,y,z]
Alternate :
"integrate x+y+z dx dy dz"
Math Input :
Klik di sini

Integrate[(1-xyz)/(2x+3y-z) dx dy dz]

Wolfram Language :
Integrate[Divide[1-xyz,(2x+3y-z)],x,y,z]
Alternate :
Integrate[(1-xyz)/((2x+3y-z)),x,y,z] or "integrate (1-xyz)/((2x+3y-z)) dx dy dz"
Math Input :
Klik di sini

8. Integral Tentu (Definite Integral)

Integrate[{1,3} x^4 dx]

Wolfram Language :
Integrate[Power[x,4],{x,1,3}]
Alternate :
Integrate[x^4,{x,1,3}]
Math Input :
Klik di sini

Integrate[{0,2} 5x^3 dx]

Wolfram Language :
Integrate[5Power[x,3],{x,0,2}]
Alternate :
Integrate[5x^3,{x,0,2}]
Math Input :
Klik di sini

Integrate[{0,5} x^3+5x^2 dx]

Wolfram Language :
Integrate[Power[x,3]+5Power[x,2],{x,0,5}]
Alternate :
Integrate[x^3+5x^2,{x,0,5}]
Math Input :
Klik di sini

Integrate[{2,4} x^3+5x^2 dx]

Wolfram Language :
Integrate[3Power[x,2]-6x,{x,2,4}]
Alternate :
Integrate[3x^2-6x,{x,2,4}]
Math Input :
Klik di sini

Integrate[{1,4} 3^x dx]

Wolfram Language :
Integrate[Power[3,x],{x,1,4}]
Alternate :
Integrate[3^x,{x,1,4}]
Math Input :
Klik di sini

Integrate[{1,2} (2x^5-x+3)/x^2 dx]

Wolfram Language :
Integrate[Divide[2Power[x,5]-x+3,Power[x,2]],{x,1,2}]
Alternate :
Integrate[(2x^5-x+3)/x^2,{x,1,2}]
Math Input :
Klik di sini

Integrate[{0,1} 32/(x^2-64) dx]

Wolfram Language :
Integrate[Divide[32,Power[x,2]-64],{x,0,1}]
Alternate :
Integrate[32/(x^2-64),{x,0,1}]
Math Input :
Klik di sini

Integrate[{2,3} 1/sqrt(x-1) dx]

Wolfram Language :
Integrate[Divide[1,Sqrt[x-1]],{x,2,3}]
Alternate :
Integrate[1/sqrt(x-1),{x,2,3}] or Integrate[1/√(x-1),{x,2,3}]
Math Input :
Klik di sini

Integrate[{0,1} x^x dx]

Wolfram Language :
Integrate[Power[x,x],{x,0,1}]
Alternate :
Integrate[x^x,{x,0,1}]
Math Input :
Klik di sini

Integrate[{0,∞} e^(-t)t^4 dt]

Wolfram Language :
Integrate[Power[e,-t]Power[t,4],{t,0,∞}]
Alternate :
Integrate[e^(-t)t^4,{t,0,∞}] or Integrate[e^(-t)t^4,{t,0,infinity}]
Math Input :
Klik di sini

Integrate[{5,∞} e^(-t)/t dt]

Wolfram Language :
Integrate[Divide[Power[e,-t],t],{t,5,∞}]
Alternate :
Integrate[e^(-t)/t,{t,5,∞}] or Integrate[e^(-t)/t,{t,5,infinity}]
Math Input :
Klik di sini

Integrate[{0,π/2} cos(x)+sin(x) dx]

Wolfram Language :
Integrate[Cos[x]+Sin[x],{x,0,Divide[π,2]}]
Alternate :
Integrate[cos(x)+sin(x),{x,0,π/2}] or Integrate[cos(x)+sin(x),{x,0,pi/2}]
Math Input :
Klik di sini

Integrate[{0,π/2} sin^3(cos(x)) dx]

Wolfram Language :
Integrate[Power[Sin[Cos[x]],3],{x,0,Divide[π,2]}]
Alternate :
Integrate[sin^3(cos(x)),{x,0,π/2}] or Integrate[sin^3(cos(x)),{x,0,pi/2}]
Math Input :
Klik di sini

Integrate[{0,π} cos(x^2) dx]

Wolfram Language :
Integrate[Cos[Power[x,2]],{x,0,π}]
Alternate :
Integrate[cos(x^2),{x,0,π}] or Integrate[cos(x^2),{x,0,pi}]
Math Input :
Klik di sini

Integrate[{1,π} sin⁡(x)/x+cos⁡(x)/x dx]

Wolfram Language :
Integrate[Divide[Sin⁡[x],x]+Divide[Cos[x],x],{x,1,π}]
Alternate :
Integrate[sin⁡(x)/x+cos⁡(x)/x,{x,1,π}] or Integrate[sin⁡(x)/x+cos⁡(x)/x,{x,1,pi}]
Math Input :
Klik di sini

Integrate[{π/2,π} sqrt(sin⁡(x)+cos⁡(x)) dx]

Wolfram Language :
Integrate[Sqrt[Cos[x]+Sin[x]],{x,Divide[π,2],π}]
Alternate :
Integrate[sqrt(sin⁡(x)+cos⁡(x)),{x,π/2,π}] or Integrate[√(sin⁡(x)+cos⁡(x)),{x,pi/2,pi}]
Math Input :
Klik di sini

Integrate[{0,π} sin(sin(x)) dx]

Wolfram Language :
Integrate[Sin[Sin[x]],{x,0,π}]
Alternate :
Integrate[sin(sin(x)),{x,0,π}] or Integrate[sin(sin(x)),{x,0,pi}]
Math Input :
Klik di sini

Integrate[{0,∞} (xln⁡(x))/(e^(2πx)-1) dx]

Wolfram Language :
Integrate[Divide[xLog[x],Power[e,2πx]-1],{x,0,∞}]
Alternate :
Integrate[(xlog⁡(x))/(e^(2πx)-1),{x,0,∞}] or Integrate[(xlog⁡(x))/(e^(2pix)-1),{x,0,infinity}]
Math Input :
Klik di sini

Integrate[{2,3} sqrt(ln⁡(x)) dx]

Wolfram Language :
Integrate[Sqrt[Log[x]],{x,2,3}]
Alternate :
Integrate[sqrt(log(x)),{x,2,3}] or Integrate[√(log⁡(x)),{x,2,3}]
Math Input :
Klik di sini

Integrate[{0,1} sqrt((1-t^2/4)/(1-t^2)) dt]

Wolfram Language :
Integrate[Sqrt[Divide[1-Divide[Power[t,2],4],1-Power[t,2]]],{t,0,1}]
Alternate :
Integrate[sqrt((1-t^2/4)/(1-t^2)),{t,0,1}] or Integrate[√((1-t^2/4)/(1-t^2)),{t,0,1}]
Math Input :
Klik di sini

Integrate[{-2,2} (x^3cos⁡(x/2)+1/2)sqrt(4-x^2) dx]

Wolfram Language :
Integrate[(Power[x,3]Cos[Divide[x,2]]+Divide[1,2])sqrt[4-Power[x,2]],{x,-2,2}]
Alternate :
Integrate[(x^3cos⁡(x/2)+1/2)sqrt(4-x^2),{x,-2,2}] or Integrate[(x^3cos⁡(x/2)+1/2)√(4-x^2),{x,-2,2}]
Math Input :
Klik di sini

9. Integral Ganda Tentu (Definite Double Integral)

Integrate[{0,1}{0,1} x+y dx dy]

Wolfram Language and Alternate :
Integrate[x+y,{x,0,1},{y,0,1}]
Math Input :
Klik di sini

Integrate[{1,2}{0,1} xy^2 dx dy]

Wolfram Language :
Integrate[x Power[y,2],{x,0,1},{y,1,2}]
Alternate :
Integrate[xy^2,{x,0,1},{y,1,2}]
Math Input :
Klik di sini

Integrate[{0,1}{0,1} x^2/(1+y^2) dx dy]

Wolfram Language :
Integrate[Divide[Power[x,2],1+Power[y,2]],{x,0,1},{y,0,1}]
Alternate :
Integrate[x^2/(1+y^2),{x,0,1},{y,0,1}]
Math Input :
Klik di sini

Integrate[{0,1}{0,1} x/(xy+1)^2 dx dy]

Wolfram Language :
Integrate[Divide[x,Power[xy+1,2]],{x,0,1},{y,0,1}]
Alternate :
Integrate[x/(xy+1)^2,{x,0,1},{y,0,1}]
Math Input :
Klik di sini

Integrate[{0,1}{0,1} sqrt((1-x^2)(1-y^2)) dx dy]

Wolfram Language :
Integrate[Sqrt[(1-Power[x,2])(1-Power[y,2])],{x,0,1},{y,0,1}]
Alternate :
Integrate[sqrt((1-x^2)(1-y^2)),{x,0,1},{y,0,1}] or Integrate[√((1-x^2)(1-y^2)),{x,0,1},{y,0,1}]
Math Input :
Klik di sini

Integrate[{0,1}{0,y^2} 3y^3 e^(xy) dx dy]

Wolfram Language :
Integrate[3Power[y,3]Power[e,xy],{x,0,Power[y,2]},{y,0,1}]
Alternate :
Integrate[3y^3 e^(xy),{x,0,y^2},{y,0,1}]
Math Input :
Klik di sini

Integrate[{0,π}{x,π} sin⁡(y)/y dx dy]

Wolfram Language :
Integrate[Divide[Sin⁡[y],y],{x,x,π},{y,0,π}]
Alternate :
Integrate[sin⁡(y)/y,{x,x,π},{y,0,π}] or Integrate[sin⁡(y)/y,{x,x,pi},{y,0,pi}]
Math Input :
Klik di sini

Integrate[{0,π/2}{0,π/2} sin⁡(y)/y dx dy]

Wolfram Language :
Integrate[xCos[xy],{x,0,Divide[π,2]},{y,0,Divide[π,2]}]
Alternate :
Integrate[xcos(xy),{x,0,π/2},{y,0,π/2}] or Integrate[xcos(xy),{x,0,pi/2},{y,0,pi/2}]
Math Input :
Klik di sini

Integrate[{0,1}{0,1} ln⁡(xy)/(1-xy) dx dy]

Wolfram Language :
Integrate[Divide[Log[xy],1-xy],{x,0,1},{y,0,1}]
Alternate :
Integrate[log⁡(xy)/(1-xy),{x,0,1},{y,0,1}] or Integrate[log⁡(xy)/(1-xy),{x,0,1},{y,0,1}]
Math Input :
Klik di sini

Integrate[{0,∞}{0,∞} 1/sqrt((1+x^4)(1+y^4)) dx dy]

Wolfram Language :
Integrate[Divide[1,Sqrt[(1+Power[x,4])(1+Power[y,4])]],{x,0,∞},{y,0,∞}]
Alternate :
Integrate[1/sqrt((1+x^4)(1+y^4)),{x,0,∞},{y,0,∞}] or Integrate[1/√((1+x^4)(1+y^4)),{x,0,infinity},{y,0,infinity}]
Math Input :
Klik di sini

10. Integral Rangkap Tiga Tentu (Definite Triple Integral)

Integrate[{0,1}{0,1}{0,1} xy+xz+yz dx dy dz]

Wolfram Language and Alternate :
Integrate[xy+xz+yz,{x,0,1},{y,0,1},{z,0,1}]
Math Input :
Klik di sini

Integrate[{0,1}{0,1}{0,1} (x^2 y^3)/(1-z(1-xy)) dx dy dz]

Wolfram Language :
Integrate[Divide[(Power[x,2]Power[y,3]),(1-z(1-xy))],{x,0,1},{y,0,1},{z,0,1}]
Alternate :
Integrate[(x^2 y^3)/(1-z(1-xy)),{x,0,1},{y,0,1},{z,0,1}]
Math Input :
Klik di sini

Integrate[{0,6}{0,3-x/2}{0,1/3(6-x-2y)} x+y+z dz dy dx]

Wolfram Language :
Integrate[x+y+z,{x,0,6},{y,0,3-Divide[x,2]},{z,0,Divide[1,3](6-x-2y)}]
Alternate :
Integrate[x+y+z,{x,0,6},{y,0,3-x/2},{z,0,1/3(6-x-2y)}]
Math Input :
Klik di sini

Integrate[{0,4}{0,1}{2y,2} (4cos⁡(x^2))/(2sqrt(z)) dx dy dz]

Wolfram Language :
Integrate[Divide[(4 Cos⁡[Power[x,2]]),(2 Sqrt[z])],{z,0,4},{y,0,1},{x,2y,2}]
Alternate :
Integrate[(4cos⁡(x^2))/(2sqrt(z)),{z,0,4},{y,0,1},{x,2y,2}] or Integrate[(4cos⁡(x^2))/(2√z),{z,0,4},{y,0,1},{x,2y,2}]
Math Input :
Klik di sini

G. Transformasi

Transformasi di sini seperti Transformasi Laplace dan Transformasi Fourier beserta juga dengan Inversnya.

1. Transformasi Laplace (Laplace Transform)

L_t{1}(s)

Wolfram Language and Alternate :
LaplaceTransform[1,t,s]
Math Input :
Klik di sini

L_x{1/sqrt(x)}(s)

Wolfram Language :
LaplaceTransform[Divide[1,Sqrt[x]],x,s]
Alternate :
LaplaceTransform[1/sqrt(x),x,s] or LaplaceTransform[1/√x,x,s]
Math Input :
Klik di sini

L_x{x^n}(s)

Wolfram Language :
LaplaceTransform[Power[x,n],x,s]
Alternate :
LaplaceTransform[x^n,x,s]
Math Input :
Klik di sini

L_x{e^(x/2)}(s)

Wolfram Language :
LaplaceTransform[Power[e,Divide[x,2]],x,s]
Alternate :
LaplaceTransform[e^(x/2),x,s]
Math Input :
Klik di sini

L_t{sin⁡(tx)}(s)

Wolfram Language :
LaplaceTransform[Sin[tx],t,s]
Alternate :
LaplaceTransform[sin⁡(tx),t,s]
Math Input :
Klik di sini

L_t{cos(tx)}(s)

Wolfram Language :
LaplaceTransform[Cos[tx],t,s]
Alternate :
LaplaceTransform[cos(tx),t,s]
Math Input :
Klik di sini

L_t{e^(-2t) sin^2⁡(t)}(s)

Wolfram Language :
LaplaceTransform[Power[e,-2t]Power[Sin[t],2],t,s]
Alternate :
LaplaceTransform[e^(-2t) sin^2⁡(t),t,s]
Math Input :
Klik di sini

L_t{t^4 cos⁡(t)}(s)

Wolfram Language :
LaplaceTransform[Power[t,4]Cos[t],t,s]
Alternate :
LaplaceTransform[t^4 cos⁡(t),t,s]
Math Input :
Klik di sini

L_x{(x+1)/(x-1)}(s)

Wolfram Language :
LaplaceTransform[Divide[(x+1),(x-1)],x,s]
Alternate :
LaplaceTransform[(x+1)/(x-1),x,s]
Math Input :
Klik di sini

L_x{ln⁡(x)/(1-x)}(s)

Wolfram Language :
LaplaceTransform[Divide[Log[x],(1-x)],x,s]
Alternate :
LaplaceTransform[log⁡(x)/(1-x),x,s]
Math Input :
Klik di sini

L_{x, y}{xe^-y}(p, q)

Wolfram Language :
LaplaceTransform[x Exp[-y],{x,y},{p,q}]
Alternate :
LaplaceTransform[x exp(-y),{x,y},{p,q}] or LaplaceTransform[xe^-y,{x,y},{p,q}]
Math Input :
Klik di sini

https://reference.wolfram.com/language/ref/LaplaceTransform.html

https://mathworld.wolfram.com/LaplaceTransform.html

2. Invers Transformasi Laplace (Inverse Laplace Transform)

L^-1_x{1/x^3}(s)

Wolfram Language :
InverseLaplaceTransform[Divide[1,Power[x,3]],x,s]
Alternate :
InverseLaplaceTransform[1/x^3,x,s]
Math Input :
Klik di sini

L^-1_x{1/sqrt(x)}(s)

Wolfram Language :
InverseLaplaceTransform[Divide[1,Sqrt[x]],x,s]
Alternate :
InverseLaplaceTransform[1/sqrt(x),x,s] or InverseLaplaceTransform[1/√x,x,s]
Math Input :
Klik di sini

L^-1_x{x/(x-a)}(s)

Wolfram Language :
InverseLaplaceTransform[Divide[x,x-a],x,s]
Alternate :
InverseLaplaceTransform[x/(x-a),x,s]
Math Input :
Klik di sini

L^-1_t{t/(t^2+x)}(s)

Wolfram Language :
InverseLaplaceTransform[Divide[t,Power[t,2]+x],t,s]
Alternate :
InverseLaplaceTransform[t/(t^2+x),t,s]
Math Input :
Klik di sini

L^-1_t{(t-a)/((t-a)^2+b)}(s)

Wolfram Language :
InverseLaplaceTransform[Divide[t-a,Power[(t-a),2]+b],t,s]
Alternate :
InverseLaplaceTransform[(t-a)/((t-a)^2+b),t,s]
Math Input :
Klik di sini

L^-1_x{ln⁡(x)/x}(s)

Wolfram Language :
InverseLaplaceTransform[Divide[Log[x],x],x,s]
Alternate :
InverseLaplaceTransform[log⁡(x)/x,x,s]
Math Input :
Klik di sini

https://reference.wolfram.com/language/ref/InverseLaplaceTransform.html

3. Transformasi Fourier (Fourier Transform)

F_t{1}(s)

Wolfram Language and Alternate :
FourierTransform[1,t,s]
Math Input :
Klik di sini

F_x{x^2}(s)

Wolfram Language :
FourierTransform[Power[x,2],x,s]
Alternate :
FourierTransform[x^2,x,s]
Math Input :
Klik di sini

F_x{1/sqrt(x)}(s)

Wolfram Language :
FourierTransform[Divide[1,Sqrt[x]],x,s]
Alternate :
FourierTransform[1/sqrt(x),x,s] or FourierTransform[1/√x,x,s]
Math Input :
Klik di sini

F_t{1/(1+t^2)}(s)

Wolfram Language :
FourierTransform[Divide[1,1+Power[t,2]],t,s]
Alternate :
FourierTransform[1/(1+t^2),t,s]
Math Input :
Klik di sini

F_t{e^(-t^2)}(s)

Wolfram Language :
FourierTransform[Power[e,-Power[t,2]],t,s]
Alternate :
FourierTransform[e^(-t^2),t,s]
Math Input :
Klik di sini

F_t{cos^2(t)}(s)

Wolfram Language :
FourierTransform[Power[Cos[t],2],t,s]
Alternate :
FourierTransform[cos^2(t),t,s]
Math Input :
Klik di sini

F_t{sin⁡(t^2)}(s)

Wolfram Language :
FourierTransform[Sin[Power[t,2]],t,s]
Alternate :
FourierTransform[sin⁡(t^2),t,s]
Math Input :
Klik di sini

F_x{sin⁡(x)+cos⁡(x)}(s)

Wolfram Language :
FourierTransform[Sin[x]+Cos[x],x,s]
Alternate :
FourierTransform[sin⁡(x)+cos⁡(x),x,s]
Math Input :
Klik di sini

F_{x, y}{1/sqrt(x^2+y^2)}(u, v)

Wolfram Language :
FourierTransform[Divide[1,Sqrt[Power[x,2]+Power[y,2]]],{x,y},{u,v}]
Alternate :
FourierTransform[1/sqrt(x^2+y^2),{x,y},{u,v}] or FourierTransform[1/√(x^2+y^2),{x,y},{u,v}]
Math Input :
Klik di sini

https://reference.wolfram.com/language/ref/FourierTransform.html

https://mathworld.wolfram.com/FourierTransform.html

4. Invers Transformasi Fourier (Inverse Fourier Transform)

F^-1_t{1}(s)

Wolfram Language and Alternate :
InverseFourierTransform[1,t,s]
Math Input :
Klik di sini

F^-1_x{x^2}(s)

Wolfram Language :
InverseFourierTransform[Power[x,2],x,s]
Alternate :
InverseFourierTransform[x^2,x,s]
Math Input :
Klik di sini

F^-1_t{1/(t+1)}(s)

Wolfram Language :
InverseFourierTransform[Divide[1,(t+1)],t,s]
Alternate :
InverseFourierTransform[1/(t+1),t,s]
Math Input :
Klik di sini

F^-1_x{e^(-x^2)}(s)

Wolfram Language :
InverseFourierTransform[Exp[Power[-x,2]],x,s]
Alternate :
InverseFourierTransform[exp(-x^2),x,s] or InverseFourierTransform[e^(-x^2),x,s]
Math Input :
Klik di sini

F^-1_x{sin⁡(x)+cos⁡(x)}(s)

Wolfram Language :
InverseFourierTransform[Sin[x]+Cos[x],x,s]
Alternate :
InverseFourierTransform[sin⁡(x)+cos⁡(x),x,s]
Math Input :
Klik di sini

F^-1_x{ln⁡(x)}(s)

Wolfram Language :
InverseFourierTransform[Log[x],x,s]
Alternate :
InverseFourierTransform[log⁡(x),x,s]
Math Input :
Klik di sini

https://reference.wolfram.com/language/ref/InverseFourierTransform.html

Untuk melihat Postingan Artikel terdahulu di Blog ini, silakan lihat di sini. Dan untuk melihat Artikel ini di Part 1, silakan lihat di sini.

Jadi jika dulu (Sebelum Juli 2021), kita harus mempelajari Bahasa Wolfram (Wolfram Language) terlebih dahulu untuk memasukkan (Input) Rumus-rumus Matematika yang Rumit dan Kompleks. Kini, tak perlu ribet lagi karena sudah ada Math Input di Wolfram|Alpha.

Dan sebenarnya, Wolfram|Alpha itu tidak hanya digunakan untuk Matematika saja, tapi bisa juga untuk Fisika, Kimia, Biologi, Geografi, Ekonomi (Keuangan), Sejarah, Sosiologi, Bahasa, hingga Kehidupan Sehari-hari seperti Sistem Penanggalan, Ensiklopedia, Hiburan, hingga Situasi Dunia saat ini. Jadi Wolfram Alpha itu bisa seperti Google, hanya saja tidak bisa seperti Mesin Pencarian Google.

Terima Kasih 😄😘👌👍 :)

Wassalamu‘alaikum wr. wb.