Evaluate: `int_0^(pi/2)log((4+3sinx)/(4+3cosx))dx`

Explanation

Let `I=int_(0)^((pi)/2)log((4+3sinx)/(4+3cosx))dx`……………1
`=int_(0)^((pi)/2)log[(4+3sin((pi)/2-x))/(4+3cos((pi)/2-x))]dx`
`=int_(0)^((pi)/2)log((4+3cosx)/(4+3cosx))dx`……………..2
Adding 1 and 2 we get
`2I=int_(0)^((pi)/2){log((4+3sinx)/(4+3cosx))+log((4+3cosx)/(4+3sinx))}dx`
`=int_(0)^((pi)/2)log((4+3sinx)/(4+3cosx)xx(4+3cosx)/(4+3sinx))dx`
`=int_(0)^(pi//2)log1 dx=0`
or `I=0`