After some integration process, I ended up with the following expression:
(1/(b (-1 + E^b) Re[b]))E^-Re[b]( b E^b - b + E^Re[b] Re[b] - E^(b + Re[b]) Re[b] + E^Re[b] Sqrt[E^(-2 b) (-1 + E^b)^2] Re[b] + b E^(b + Re[b]) Sqrt[E^(-2b)(-1 + E^b)^2] Re[b] )
all is good, but this expression is supposed to be equal to
1 + (2/b) e^(-b) - 1/b
via simple numerical trials, i can confirm that they are equal. But, it would be great if I can actually make Mathematica simplify that nasty expression into this innocent form.
Fullsimplify, it does not work. Does anyone have any suggestion?
bis Real, if not, dont use the
Assumptions) in your integration process. it might save you some time. $\endgroup$