Indefinite Integration

$\frac{1}{5} \log \left|\tan \left(\frac{x}{2}+\frac{\alpha}{2}\right)\right|+c$

$\frac{1}{5} \log \left|\tan \left(\frac{\pi}{4}+\frac{x}{2}+\frac{\alpha}{2}\right)\right|+c$

$\frac{1}{5} \log \left|\tan \left(\frac{\pi}{4}-\frac{x}{2}-\frac{\alpha}{2}\right)\right|+c$

$\frac{1}{5} \log |\tan (\sec x+\tan x)|+c$