Re: An exact 1-D integration challenge - 23

int(z/(sin(z)^2*(sqrt(cot(z))+cot(z))), z= 0..Pi/2);

How about


3/16*I*Pi^2-1/2*I*arctan(2^(1/2)/(2+2^(1/2)))*Pi+2*I*dilog(1/2*2^(1/2)/(-
2+2^(1/2))+1/2*I*2^(1/2)/(-2+2^(1/2))-1/(-2+2^(1/2)))-2*I*dilog(1/2*2^(1
/2)/(2+2^(1/2))-1/2*I*2^(1/2)/(2+2^(1/2))+1/(2+2^(1/2)))+1/4*I*ln(2)*ln(
2-2^(1/2))-1/4*I*ln(2+2^(1/2))*ln(2)-1/16*Pi*ln(1/32/(768398401+54333972
0*2^(1/2)))-3/2*arctan(2^(1/2)/(2+2^(1/2)))*ln(2)

evalf(%);
2.397347715

(You only asked to evaluate it, not to simplify the answer...)

A change of variables converted the problem to:

Int(4*u*ln(u+1)/(1+u^4),u=0..infinity);

and then Maple could evaluate that.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.