Question

Evaluate : $\sqrt{1+\cos x}dx$

Answer 1

$\int \sqrt{1+cosx}dx$

$=\int \sqrt{2{\cos }^{2}x/2}dx[\because cosx=2{\cos }^{2}x/2-1]$

$=\int \sqrt{2}cosx/2dx$

$=\sqrt{2}\int cosx/2dx$

$=\sqrt{2}\frac{sinx/2}{1/2}+c$

$=2\sqrt{2}sinx/2+c$