Re: Integration by substitution

*To*: mathgroup at smc.vnet.net*Subject*: [mg29852] Re: [mg29800] Integration by substitution*From*: "Mark Harder" <harderm at ucs.orst.edu>*Date*: Fri, 13 Jul 2001 04:19:33 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Gregory, Regarding the 2nd integral. Which of these two did you have in mind? A.) Integrate[a Sech[sp]^2 Sech[(tp - sp)]^2, {sp, -Infinity, Infinity}] Out[410]= (8*a*E^(2*tp)*(2 - 2*E^(2*tp) + (1 + E^(2*tp))*Log[E^(2*tp)]))/(-1 + E^(2*tp))^3 OR B.) sp = s/a; Integrate[a Sech[sp]^2 Sech[(tp - sp)]^2, {sp, -Infinity, Infinity}] \!\(\* RowBox[{\(Integrate::"ilim"\), ":", "\<\"Invalid integration variable or limit(s) in \\!\\({s\\/a, \ \\*InterpretationBox[\\(-\[Infinity]\\), DirectedInfinity[-1]], \ \\*InterpretationBox[\\\"\[Infinity]\\\", DirectedInfinity[1]]}\\) .\"\>"}]\) Out[412]= Integrate[a*Sech[s/a]^2*Sech[s/a - tp]^2, {s/a, -Infinity, Infinity}] i.e. Mathematica *does* see that sp=s/a when you tell it that,& it makes the substitution, but evidently it won't integrate over a function (expression) like s/a, so it tells you that. Probably, you will have to tell Mathematica to expand the differential in the integral. I don't know how to do this, however. -mark harder -----Original Message----- From: G. A. Garrett <ggarrett7 at netscape.net> To: mathgroup at smc.vnet.net Subject: [mg29852] [mg29800] Integration by substitution >I was wondering if someone could explain to me why the first input >below gives no answer while the second input does. It never crossed my >mind the Mathematica wouldn't have seen the simple substitution of >sp=s/a that produced an answer. I am running ver. 4.0 in a Windows >environment. I am basically looking for a characteristic that I can be >on the look out for in the future. > >Integrate[Sech[s/a]^2 Sech[(t - s)/a]^2, {s, -Infinity, Infinity}] > >Integrate[a Sech[sp]^2 Sech[(tp - sp)]^2, {sp, -Infinity, Infinity}] > >Gregory >--Posted email rarely checked-- >