Re: Integration by substitution

*To*: mathgroup at smc.vnet.net*Subject*: [mg29843] Re: Integration by substitution*From*: Ignacio Rodriguez <ignacio at sgirmn.pluri.ucm.es>*Date*: Fri, 13 Jul 2001 04:19:23 -0400 (EDT)*Organization*: UCM*References*: <200107110025.UAA20901@smc.vnet.net> <9iji2g$rik$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Dear Mr Rockmann, It is true that "sp" and "tp" are single variables, but under the substitution sp->s/a and tp->t/a, the 2 expressions Integrate[Sech[s/a]^2 Sech[(t - s)/a]^2, {s, -Infinity, Infinity}] and Integrate[a Sech[sp]^2 Sech[(tp - sp)]^2, {sp, -Infinity, Infinity}] are mathematically equivalent. This can be checked by substituting and taking into account that ds = a dsp and that the integration limits do not change. J Rockmann wrote: > ----- Original Message ----- > From: "G. A. Garrett" <ggarrett7 at netscape.net> To: mathgroup at smc.vnet.net > Subject: [mg29843] 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-- > > > If I'm not mistaken, Mathematica will consider "sp" as a single variable as > it would "x". Therefore, the two statements are not equivalent to > Mathematica after any algebraic manipulation has been performed on your > naming of the variable "sp=sa". > I hope this helps, > Jonathan Rockmann > mtheory at msn.com -- Ignacio Rodriguez Ramirez de Arellano Unidad de RMN Universidad Complutense Paseo Juan XXIII, 1 Madrid 28040, Spain Tel. 34-91-394-3288 Fax 34-91-394-3245 e-mail: ignacio at sgirmn.pluri.ucm.es

**References**:**Integration by substitution***From:*ggarrett7@netscape.net (G. A. Garrett)