Wrong:
(%i32) integrate(atan2(1,x),x,-1,1); (%o32) -(2*log(2)+%pi)/4+log(2)/2-(3*%pi)/4 (%i33) float(%); (%o33) -3.141592653589793
The range of x --> atan2(1,x)
is (0, %pi)
, so the value of integrate(atan2(1,x),x,-1,1)
is positive; specifically, the correct value is %pi.
Diff: