Evaluate:
Question:

Evaluate: $\int x \sqrt{x+2} d x$

Solution:

Here Add and subtract 2 from $x$

We get

$\Rightarrow \int(x+2-2) \sqrt{x+2} d x$

$\Rightarrow \int(x+2)^{\frac{3}{2}} d x-\int 2 \sqrt{x+2} d x$

$\Rightarrow \frac{2(x+2)^{\frac{5}{2}}}{5}-\frac{4(x+2)^{\frac{3}{2}}}{3}+c$