# [Maxima] problem with integration of gaussian distribution

Riemann, Robert robert.riemann at physik.hu-berlin.de
Mon Jul 6 14:20:50 CDT 2009

```Thanks for your both help.

Maxima computes the integration.
The result may be right, but is to complicated to interpret.
Exponentialze doesnt seem to work for this solution.

I thought i could help maxima with some "wise" ;)
substitutions.
I found out that Maxima solves something like this as expected:
integrate(exp(-x^2-2*x),x,minf,inf);

What must I do, to let Maxima sort some summands in powers of p?
Is it possible to force Maxima to use a given substitution to make the terms
easier?

Greets Robert

Am Montag, 6. Juli 2009 18:03:45 schrieb Leo Butler:
> On Mon, 6 Jul 2009, Robert Riemann wrote:
>
> < Hi all,
> <
> < i have problems to get Maxima solve an integral about a
> < bell-shaped curve with a weighting function phi.
> <
> < I tried it with the following code:
> <
> < assume( m > 0, d > 0, h > 0, A > 0)\$
> < phi(p) := A*exp(-(p-p_0)^2/(h/d)^2);
> < psi(x,t) :=
> integrate(phi(p)*(2*%pi*h)^(-1)*exp(%i/h*(p*x-p^2/(2*m)*t)),p,minf,inf);
>
> Note that x does not appear in the rhs. Also, I think you want to write
>
> integrate(...)\$
> psi(x,t) := ''%;
>
> This will compute the integral once.
>
> <
> < The result should be a bell-shaped curve to.
> <
> < What do i have to do to get a human-friendly solution (not with sin, cos,
> but exp) of this integral? < Is this possible with maxma/wxmaxima?
>
> Try:
> integrate(...)\$
> %,exponentialize\$
> psi(x,t) := ''%;
>
> The second line does what it says.
>
> Leo

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