Re: troubling simple integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg91364] Re: troubling simple integral*From*: did <didier.oslo at hotmail.com>*Date*: Mon, 18 Aug 2008 03:37:25 -0400 (EDT)*References*: <g86844$hr7$1@smc.vnet.net> <g88v87$gva$1@smc.vnet.net>

On Aug 17, 12:41 pm, Jean-Marc Gulliet <jeanmarc.gull... at gmail.com> wrote: > Does the following result look better? > > In[1]:= Assuming[x > 0 && Im[a] == 0 && Im[b] == 0 && Im[y] == = 0, > FullSimplify[ > Integrate[(b + k*x)/k^2*Exp[-k*x]*Sin[k*a]*Sin[k*y], {k, 0, > Infinity}]]] > > Out[1]= 1/4 (2 b ((-a + y) ArcTan[(a - y)/x] + (a + y) ArcTan[(a + y)/ > x] - x ArcTanh[(2 a y)/(a^2 + x^2 + y^2)]) + > x Log[1 + (4 a y)/(x^2 + (a - y)^2)]) That looks much better indeed. Thanks. > Note that *Assuming* passes the assumptions to both Integrate[] *and* > FullSimplify[]. (In your original expression, only Integrate[] could > take into account the assumptions.) I understand that. But what I find puzzling the result obtained by Alberto (I got the same). I'm wondering if there is an issue there.