How can I integrate indefinite integral $\int\frac{1}{a+b\sin x}dx$?

Question

I tried taking hints from this How do you integrate $\int \frac{1}{a + \cos x} dx$? but could not find answer.

I am learning integration from book and youtube videos, so answers with explanation would be of great help to me.

Answer 1

$$\frac{1}{a+b\sin x} = \frac{1}{b}\cdot \frac{1}{\frac ab + \sin x}$$

Now, use the methods in the question you linked.