Question

How do you integrate `int x(x+1)^8` using substitution?

Answer 1

`(x+1)^10/10-(x+1)^9/9+C`

Explanation:

Substitute `u=x+1` and you get:
`int(u-1)u^8du`
`=int u^9du - int u^8du`
`=u^10/10-u^9/9+C`
Substituting back `u=x+1` gives the answer.