Question

What is the antiderivative of `(x+1)^2`?

Answer 1

`int (x+1)^2 d x=1/3 (x+1)^3+C`

Explanation:

`int (x+1)^2 d x=?`

`x+1=u" ; "d x=d u`

`int (x+1)^2=int u^2 *d u`

`"so " int u^2 d u=1/3 u^3 +C`

`int (x+1)^2 d x=1/3 u^3+C`

`int (x+1)^2 d x=1/3 (x+1)^3+C`