Question

Solve:
$\int \frac{1}{\sin x\sqrt{\sin x\cos x}}dx=$

Answer 1

$\int \frac{1}{\sin x\sqrt{\sin x\cos x}}dx=\int \frac{1}{{\sin }^{3/2}x{\cos }^{1/2}x}\times \frac{{\cos }^{3/2}x}{{\cos }^{3/2}x}dx=\int \frac{{\sec }^{2}x}{{\tan }^{3/2}x}dx=2\sqrt{tanx}+c$