Evaluate the following integral: `int_(pi//3)^(pi//2)(sqrt(1+cosx))/((1-cosx)^(3//2))dx`

Explanation

Let I=`int_(pi//3)^(pi//2)(sqrt(1+cosx))/((1-cosx)^(3//2))dx`


I=`int_(pi//3)^(pi//2)(sqrt(1+cosx))/((1-cosx)^(3//2)) xx(sqrt(1-cosx))/(sqrt(1-cosx))dx`

I=`int_(pi//3)^(pi//2) sinx/cosxdx`

I=`int_(pi//3)^(pi//2) tanxdx`

=`tan(pi/2)-tan(pi/3)`

=`-tan(pi/3)`