Question

$\int \sqrt{2x}.\cos 2xdx$

Answer 1

$\begin{array}{c}{\int }^{}\sqrt{2x}\cos 2x={\int }^{}\sqrt{2}\sqrt{x}\cos \left(2x\right)dx\\ =\frac{\sqrt{x}\sin \left(2x\right)}{2}-{\int }^{}\frac{\sin \left(2x\right)}{4\sqrt{x}}dx\\ =\frac{\sqrt{x}\sin \left(2x\right)}{2}-\frac{\sqrt{\pi }S\left(\frac{2\sqrt{x}}{\sqrt{\pi }}\right)}{4}\left(WhereSisFresnalIntegral\right)\end{array}$