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\int x\sqrt{x+2}dx

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

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

Unlock this step-by-step solution!

Answer

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

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

Main topic:

Integration by substitution

Used formulas:

3. See formulas

Time to solve it:

~ 0.52 seconds