1. ## Please solve this Integration problem,

$\int\frac{tan\frac{x}{2}}{1+tan^{2}\frac{x}{2}}
$

any help will be appreciated, thanks

2. $\frac{\tan\frac{x}{2}}{1+\tan^{2}\frac{x}{2}}$ $=\frac{\sin\frac{x}{2}\cos\frac{x}{2}}{\cos^2\frac {x}{2}+\sin^2\frac{x}{2}}=\sin\frac{x}{2}\cos\frac {x}{2}=\frac{\sin x}{2}$ so $\int\frac{\tan\frac{x}{2}}{1+\tan^{2}\frac{x}{2}}d x=-\frac{\cos x}{2}+C$