Question

please help me...........​

Answer 1

Answer:

$\int \frac{x + sin(x) }{1 + \cos(x) }dx = \int \frac{x + 2sin\frac{x}{2}cos \frac{x}{2} }{ {cos}^{2} \frac{x}{2} }dx = x {sec}^{2} \frac{x}{2} + 2tan \: \frac{x}{2}$

$\int d(x \tan( \frac{x}{2} ) ) = x \tan( \frac{x}{2} ) = . \frac{\pi}{2} \tan( \frac{\pi}{4} ) = \frac{\pi}{2}$