Question

Integration(0 to pi/2) x/sinx+cosx

Answer 1

in the numerator that should be   sin x.
denominator is   sin x + cos x

rewrite that numerator  as :  1/2 * [ sin x + cos x + sin x - cos x]

integrand is  1/2 -  1/2 * [ cos x - sin x]/[sin x + cos x]

integral is = x/2  - 1/2  * Log  | sin x + cos x  |

value after substituting the limits :
            π/4