Question

How do you integrate by substitution `int x^2(x^3-1)^4 dx`?

Answer 1

THe answer is `(x^3-1)^5/15+C`

Explanation:

Let `u=(x^3-1)`
Then `du=3x^2dx` `=>` `(du)/3=x^2dx`
So `intx^2(x^3-1)^4dx=int(u^4du)/3`
`=1/3*u^5/5=u^5/15`
`:.intx^2(x^3-1)^4dx=(x^3-1)^5/15+C`