Question

Solve: $\int \sqrt{\frac{1-x}{1+x}}dx$

Answer 1

$\int \sqrt{\frac{1-x}{1+x}}dx=\int \frac{1-x}{\sqrt{1-x^2}}dx=\int \frac{1}{\sqrt{1-x^2}}dx-\frac{1}{2}\int \frac{2x}{\sqrt{1-x^2}}dx\left(i_2\right)=si{n}^{-1}x+\sqrt{1-x^2}$

$i_2$ has been evaluated , reading it as $\frac{1}{2}\int \frac{dt}{\sqrt{t}}$