Question

What is the antiderivative of `(x+4)^2`?

Answer 1

`int(x+4)^2 d x=1/3(x+4)^3+C`

Explanation:

`int (x+4)^2 d x=?`

`"Substitute "u=x+4`

`d u=d x`

`int(x+4)^2 d x=int u^2*d u`

`int u^2 *d u=1/3 u^3`

`int (x+4)^2 d x=1/3 u^3`

`"Undo substitution"`

`int(x+4)^2 d x=1/3(x+4)^3+C`