Re: int(exp(x)*erf(x),x = a .. b)

From: John Creighton (JohnCreighton__at_hotmail.com)
Date: 06/14/04 

Date: 14 Jun 2004 11:41:56 -0700

JohnCreighton_@hotmail.com (John Creighton) wrote in message news:<c5e803c2.0406131138.7dfffea9@posting.google.com>...
> using MATLAB 6.1.0.450 (R12.1) to access the maple
> kernel I don't get a solution. for:
> int(exp(x)*erf(x),x = a .. b)
> Does anyone know if this is solvable? It looks like you could do parts
> a few times, and then equate terms. Since:
>
> >> int(sym('erf(x)'))
>
> ans =
>
> x*erf(x)+1/pi^(1/2)*exp(-x^2)
>
> What about the integral:
> int(exp(x^2)*erf(x),x = a .. b)
>
> For this I could let u=erf(x)
> and do substitution. Right?
>
> Moreover, If I figure out how to do the integral myself, how do I
> teach maple to do it?

Okay, Now that the above intgrals were solved how about something more
general:

int(erf(a*(x-d))*exp(-b*(x-c)^2),x = -inf .. inf)

This is really what I need to solve anyway.

P.S. Thanks for the help. Oh, yeay, I also am interested on how they
are solved. I figured out how to solve int(sym('erf(x)')) by looking
at the taylor series. of a exp(-x)^2 and erf(x) and int(erf(x)) and
just used linear algabra to see what linear combination gave the
answer.

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