Indefinite Integration

$\frac{2}{\sqrt{1+k^2}} \tan ^{-1}\left(\sqrt{\frac{1-k}{1+k}} \tan \frac{x}{2}\right)+C$

$\frac{1}{\sqrt{k^2-1}} \log \left(\frac{\sqrt{k+1}+\sqrt{k-1} \tan \frac{x}{2}}{\sqrt{k+1}-\sqrt{k-1}}\right)+C$

$\frac{1}{\sqrt{k^2+1}} \log ^{-1}\left(\frac{\sqrt{k+1}+\sqrt{k-1} \tan \frac{x}{2}}{\sqrt{k+1}-\sqrt{k-1} \tan \frac{x}{2}}\right)+C$

$\frac{1}{\sqrt{k^2-1}} \tan ^{-1}\left(\frac{\sqrt{k-1} \cos \frac{x}{2}+\sqrt{k-1} \sin \frac{x}{2}}{\sqrt{k+1} \cos \frac{x}{2}-\sqrt{k-1} \sin \frac{x}{2}}\right)+C$