Integrate the indefinite integral ?
$$\int \frac{x}{\sqrt{x^2-a^2} + \sqrt{x^2+a^2}}dx$$
My try :-
Let $x^2 = t \to 2xdx=dt$ and then rationalize
I have,
$$\frac{1}{4a^2}\int \sqrt{t-a^2}- \sqrt{t+a^2}dt$$
I know its silly, but I don't know how to get further ?
