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intintegrationlimitsmaple

Why won't Maple evaluate this integral?

restart;
assume(alph>0);
assume(alph,real);
f_exp:=exp(-alph*r^2);
ff_deriv:=simplify(r^2*f_exp^2);
ff:=simplify(int(ff_deriv,r=0..infinity));

It seems to understand what I'm trying to integrate but when I try and find ff it comes up with an awful expression full of erf functions and with a lim r--> infinity at the front. However on wolfram alpha I get the answer that I want:sqrt(pi/2)/(8*alpha^(3/2)).

Can anyone help me with this?

Thank you so much!

Solution

  • The second assume call wipes out the first assumption. As the property > 0 implies real, just drop the second assumption.

    assume(alph>0);
f_exp:=exp(-alph*r^2);
ff_deriv:=simplify(r^2*f_exp^2);
ff:=simplify(int(ff_deriv,r=0..infinity));

    Will give you the answer you want: (1/16)*sqrt(2)*sqrt(Pi)/alph^(3/2)

    You could also use additionally(alph,) if you had needed another property.