Question

$\int \frac{x+\sin x}{1+\cos x}dx$.

Answer 1

$\int \frac{x+2\sin \frac{x}{2}\cos \frac{x}{2}}{2{\cos }^2\frac{x}{2}}$

$\int (\frac{x{\sec }^2\frac{x}{2}}{2}+\tan \frac{x}{2})dx$

$x\tan \frac{x}{2}+2\ln |\cos \frac{x}{2}|-2\ln |\cos \frac{x}{2}|+C$

$x\tan \frac{x}{2}+C$