Help solving an Elliptic Integral

Question

I am facing an elliptic integral to solve during thesis, however, I'm having a lot of trouble trying to solve it. The integral is given by: $$\int{\frac{\sin^2(\theta)}{\sqrt{1+B\sin^2(\theta)}}}d\theta$$ where $B$ is a constant. I've been trying to use the Byrd and Friedman's Handbook but could not figure out some transformations that he adopts throughout the book. Any help provided will be greatly appreciated.

Answer 1

$$\frac{\sin^2(\theta)}{\sqrt{1+B\sin^2(\theta)}}=\frac{\sqrt{B \sin ^2(\theta )+1}}{B}-\frac{1}{B \sqrt{B \sin ^2(\theta )+1}}$$ $$\int{\frac{\sin^2(\theta)}{\sqrt{1+B\sin^2(\theta)}}}d\theta=\frac{E(\theta |-B)-F(\theta |-B)}{B}$$