Question

How do you integrate `(3x + 1)²`?

Answer 1

`int(3x+1)^2dx=1/9(3x+1)^3+c`

Explanation:

`int(3x+1)^2dx`, Let `u=3x+1`

`du=3dx`, so `dx=(du)/3`

Subbing `u` and `du` into the integral,

`intu^2(du)/3=1/3intu^2du=1/3[u^3/3]+c=1/9u^3+c`

`=1/9(3x+1)^3+c`