Indefinite Integration

$\frac{1}{2}\left[\sec x-\operatorname{cosec} x-\log \left|\tan \left(\frac{x}{2}\right) \tan \left(\frac{\pi}{4}+\frac{x}{2}\right)\right|\right]+C$

$\sec x-\operatorname{cosec} x+\log \left|\frac{\tan \left(\frac{\pi}{2}\right)}{\tan \left(\frac{\pi}{4}+\frac{x}{2}\right)}\right|+C$

$\frac{1}{2}\left[\sec x-\operatorname{cosec} x-\log \left|\frac{\tan \left(\frac{\pi}{4}+\frac{x}{2}\right)}{\tan \left(\frac{x}{2}\right)}\right|\right]+C$

$\sec x+\operatorname{cosec} x-\log \left|\tan \left(\frac{x}{2}\right)\right|+C$