Question

$$\int\frac{dx}{x\sqrt{2+3\sqrt{x}}}$$

Evaluate

$\frac{\sqrt{2}\ln(\frac{\left(-3\sqrt{3\sqrt{x}+2}+\sqrt{2}\right)\left(3\sqrt{3\sqrt{x}+2}-\sqrt{2}\right)}{-27\sqrt{x}-16})}{9}+С$
$x\geq 0$

Differentiate w.r.t. x

$\frac{\sqrt{\frac{2}{\left(3\sqrt{x}+2\right)x}}\left(-27sign(3\sqrt{3\sqrt{x}+2}-\sqrt{2})\sqrt{x}+27\sqrt{x}-16sign(3\sqrt{3\sqrt{x}+2}-\sqrt{2})-6\sqrt{2\left(3\sqrt{x}+2\right)}+20\right)}{4\left(3\sqrt{3\sqrt{x}+2}-\sqrt{2}\right)\left(-27\sqrt{x}-16\right)}$
$x\geq 0$