Integral antiderivative?

Question

Find the antiderivative:

⌠
⌡ x^2(3x^3-9)^7 dx

Answer 1

Differentiating (3x^3 - 9)^8
You get 8(3x^3 - 9)^7 . 9x^2 which is 72 times bigger than you need.
I hope that helps

Answer 2

Use substitution.
Let u = 3x^3-9. Then du = 9x^2 dx
So your integral is
1/9*∫ u^7 du = 1/72 u^8 = 1/72(3x³-9)^8 + C

Answer 3

Substitution Rule

let u = x^3 , then du = 3x^2 dx and
⌡ x^2(3x^3-9)^7 dx = (1/3) * ⌡ (3u - 9)^7 du