# Integrate x(x+2)^0.5

## Answer

$2\int u^{2}\left(u^{2}-2\right)du$

## Step-by-step explanation

Problem

$\int x\sqrt{x+2}dx$

1

Solve the integral $\int\sqrt{2+x}xdx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=\sqrt{2+x} \\ du=\frac{1}{2}\left(2+x\right)^{-\frac{1}{2}}dx\end{matrix}$

## Answer

$2\int u^{2}\left(u^{2}-2\right)du$