How to solve integrals of type $ \int\frac{1}{(a+b\sin x)^4}dx$ and $\int\frac{1}{(a+b\cos x)^4}dx$

Question

$$\displaystyle \int\frac{1}{(a+b\sin x)^4}dx,~~~~\text{and}~~~~\displaystyle \int\frac{1}{(a+b\cos x)^4}dx,$$

although i have tried using Trg. substution. but nothing get

Answer 1

Use $\sin(x)= \frac{2\tan\frac{x}{2}}{1 +\tan^2 \frac {x}{2}}$ and $\cos(x)= \frac{1-\tan ^{2}\frac{x}{2}}{1 +\tan^{2}\frac {x}{2}}$