Question

Solve: $\int \frac{\cos x}{1+\cos x}$

Answer 1

$\int \frac{\cos x}{1+\cos x}dx=\int \frac{2{\cos }^2\frac{x}{2}-1}{2{\cos }^2\frac{x}{2}}dx(\because \cos 2x=2{\cos }^{2}x-1)=\int [1-\frac{1}{2{\cos }^2\frac{x}{2}}]dx=\int [1-\frac{1}{2}{\sec }^2\frac{x}{2}]dx=x-\frac{1}{2}.2\tan \frac{x}{2}+C=x-\tan \frac{x}{2}+C$