Question
Evaluate the integral
x−68x2−2x6+C,C∈R
Evaluate
∫(1−17x×8−4x3×3x2)dx
Multiply the terms
∫(1−136x−4x3×3x2)dx
Multiply
More Steps

Multiply the terms
−4x3×3x2
Multiply the terms
−12x3×x2
Multiply the terms with the same base by adding their exponents
−12x3+2
Add the numbers
−12x5
∫(1−136x−12x5)dx
Use the property of integral ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx
∫1dx+∫−136xdx+∫−12x5dx
Use the property of integral ∫kdx=kx
x+∫−136xdx+∫−12x5dx
Evaluate the integral
More Steps

Evaluate
∫−136xdx
Use the property of integral ∫kf(x)dx=k∫f(x)dx
−136×∫xdx
Use the property of integral ∫xndx=n+1xn+1
−136×1+1x1+1
Simplify
More Steps

Evaluate
1+1x1+1
Add the numbers
1+1x2
Add the numbers
2x2
−136×2x2
Cancel out the common factor 2
−68x2
x−68x2+∫−12x5dx
Evaluate the integral
More Steps

Evaluate
∫−12x5dx
Use the property of integral ∫kf(x)dx=k∫f(x)dx
−12×∫x5dx
Use the property of integral ∫xndx=n+1xn+1
−12×5+1x5+1
Simplify
More Steps

Evaluate
5+1x5+1
Add the numbers
5+1x6
Add the numbers
6x6
−12×6x6
Cancel out the common factor 6
−2x6
x−68x2−2x6
Solution
x−68x2−2x6+C,C∈R
Show Solution
