# Step-by-step Solution

## Integrate $\int x\left(x+3\right)^{\left(\frac{1}{2}\right)}dx$ with respect to x

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### Videos

$\frac{2}{5}\sqrt{\left(x+3\right)^{5}}-2\sqrt{\left(x+3\right)^{3}}+C_0$

## Step-by-step explanation

Problem to solve:

$\int\left(x\left(x+3\right)^{\frac{1}{2}}\right)dx$
1

Solve the integral $\int x\sqrt{x+3}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=x+3 \\ du=dx\end{matrix}$
2

Rewriting $x$ in terms of $u$

$x=u-3$

$\frac{2}{5}\sqrt{\left(x+3\right)^{5}}-2\sqrt{\left(x+3\right)^{3}}+C_0$
$\int\left(x\left(x+3\right)^{\frac{1}{2}}\right)dx$

### Main topic:

Integration by substitution

~ 0.06 seconds