Question

Solve: $\int \sqrt{{(\cos \frac{x}{2}+\sin \frac{x}{2})}^2}dx$

Answer 1

$\int \sqrt{{(\cos \frac{x}{2}+\sin \frac{x}{2})}^2}dx=\pm [\int (\cos \frac{x}{2}+\sin \frac{x}{2})dx]=\pm 2[\sin \frac{x}{2}-\cos \frac{x}{2}]+c$