Hello all
Could any one tell me which technique is suitable to solve this integration ? i will be thankful .
Best regards
Are you looking for the integral defined over real numbers or over complex numbers? Because over real numbers, the function is not defined over large chunks of the reals. Over complex numbers, the problem becomes a little different.
Over the reals, you can do a small simplification by multiplying top and bottom by $\sqrt{\sin x \cos x}$. This will give you:
$\displaystyle \int \dfrac{\sqrt{\sin x} + \sqrt{\cos x}}{\sin x + \cos x}dx$
But, over the complex numbers, this simplification is not quite as straightforward. I am not sure I know a good technique for solving this problem.