How to integrate this using u substitution?

Question

I have another rather simple problem that I cannot seem to be able to solve. I cannot find the right substitution.

The problem is:

$$\int\frac{\sin^3{x}}{\sqrt{\cos{x}}}dx$$

I would appreciate any help...

Thank you in advance!

Answer 1

HINT:

Use a substitution $\text{u}=\cos\left(x\right)$ then the integrand changes to $-\frac{1-\text{u}^2}{\sqrt{\text{u}}}$ then substitute $\text{s}:=\sqrt{\text{u}}$ then the integrand changes to $-2\cdot\left(1-\text{s}^4\right)$

Answer 2

Put $cosx=z^2$ then $$\int\frac{\sin^3{x}}{\sqrt{\cos{x}}}dx=\int2(z^4-1)dz.$$