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

multiply by $\sec^{2}x$
then you get  

$\int \frac{\sec^{2}x}{\sqrt{\tan^{3}x}} \mathrm dx$

now let  $\tan x=t$

One gets $\int\frac{dt}{\sqrt{t^{3}}}$

Now I think u can do  it