1. Integral

The value of Definite Integral $\displaystyle \int_{0}^{\frac{\pi}{2}}(\sin x+\cos x)\sqrt{\frac{e^x}{\sin x}}dx$

2. Re: Integral

Split up the integral

$\int_0^{\pi/2} e^{x/2} \sqrt{\sin x} dx + \int_0^{\pi/2} e^{x/2} \dfrac{\cos x}{\sqrt{\sin x }}dx$

Use integration by parts on the second (choose $u = e^{x/2}$) and see what happens.