integration - How to solve this integral $int frac 1{sqrt { cos x sin^3 x }} mathrm dx $

Question : $$\int \frac 1{\sqrt { \cos x \sin^3 x }} \mathrm dx $$

I don’t know where to start. I had tried many methods but they didn’t work.

Can anyone help me solving this ?
Thank you

Answer

HINT: substitute $\text{u}:=\tan\left(x\right)$. Then the integrand will change to $\frac{1}{\text{u}^\frac{3}{2}}$.