Please integrate $\int \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a-x}} \, dx$

Evaluate the following integral
$$
\int \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a-x}} \, dx
$$
I just can’t seems to know what to do I have tried squaring out but it only gets worse.

Solutions Collecting From Web of "Please integrate $\int \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a-x}} \, dx$"

Decompose the integrand:
$$
\frac{\sqrt{x}}{\sqrt{a-x}+\sqrt{x}} =
\frac{1}{2} +
\frac{a}{2 (2 x-a)}-
\frac{\sqrt{x(a-x)}}{2 x-a}
$$
You will find
$$
\int \frac{1}{(2 x-a)} \, dx =
\frac{1}{2} \ln \left( 2x – a \right)
$$
and
$$
\int \frac{\sqrt{x(a-x)}}{2 x-a} \, dx
= \frac{1}{2} \sqrt{x(a-x)}-\frac{1}{2} a \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a-x}}\right)
$$


When successful, you will have

$$
\int \frac{\sqrt{x}}{\sqrt{a-x}+\sqrt{x}} \, dx =
\frac{1}{4} \left(2 x -2 \sqrt{x(a-x)}+a \ln (2 x-a)+2 a \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{a-x}}\right)\right)
$$