Question
Evaluate the integral
x−64x2−25x6+C,C∈R
Evaluate
∫(1−16x×8−3x3×5x2)dx
Multiply the terms
∫(1−128x−3x3×5x2)dx
Multiply
More Steps

Multiply the terms
−3x3×5x2
Multiply the terms
−15x3×x2
Multiply the terms with the same base by adding their exponents
−15x3+2
Add the numbers
−15x5
∫(1−128x−15x5)dx
Use the property of integral ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx
∫1dx+∫−128xdx+∫−15x5dx
Use the property of integral ∫kdx=kx
x+∫−128xdx+∫−15x5dx
Evaluate the integral
More Steps

Evaluate
∫−128xdx
Use the property of integral ∫kf(x)dx=k∫f(x)dx
−128×∫xdx
Use the property of integral ∫xndx=n+1xn+1
−128×1+1x1+1
Simplify
More Steps

Evaluate
1+1x1+1
Add the numbers
1+1x2
Add the numbers
2x2
−128×2x2
Cancel out the common factor 2
−64x2
x−64x2+∫−15x5dx
Evaluate the integral
More Steps

Evaluate
∫−15x5dx
Use the property of integral ∫kf(x)dx=k∫f(x)dx
−15×∫x5dx
Use the property of integral ∫xndx=n+1xn+1
−15×5+1x5+1
Simplify
More Steps

Evaluate
5+1x5+1
Add the numbers
5+1x6
Add the numbers
6x6
−15×6x6
Cancel out the common factor 3
−5×2x6
Multiply the terms
−25x6
x−64x2−25x6
Solution
x−64x2−25x6+C,C∈R
Show Solution
