Question

How do you integrate `int x (3x+1)^10` ?

Answer 1

Use substitution with `u = 3x+1`

Explanation:

`int x (3x+1)^10 dx`

Let `u = 3x+1`, so that `du = 3dx` and `x = 1/3(u-1)`

The integral becomes:

`int 1/3(u-1) u^10 1/3 du = 1/9 int (u^11-u^10) du`

The student is encouraged to finish from here.