Question

∫ √(1 + cos θ) dθ

Answer 1

Let us evaluate the integral

$\int \sqrt{1+\cos\Theta}d\Theta=\int \sqrt{2\cos^2\frac{\Theta}{2}}d\Theta= 2\sqrt{2}\int \cos\frac{\Theta}{2}d\frac{\Theta}{2}=2\sqrt{2}\sin\frac{\Theta}{2}+C$