Maxima can't solve this integral equation



Okay, this was too much to ask but still Maxima was able to help though.  The original input was

sqrt(2)*sqrt(m)*integrate(sqrt(E[n]-mu*x^4),x,-E[n]^(1/4)/mu^(1/4),E[n]^(1/4)/mu^(1/4))=%pi*hbar*(n-1/2);

After using changevar and subst and numeric integration I did finally get 

E[n]^(3/4)=((0.57206982262637*%pi*hbar*mu^(1/4)*(n-1/2))/(sqrt(2)*sqrt(m)))

which is right, I hope, or my book is wrong and me too.

Rich





 ------------Original Message------------
From: "Stavros Macrakis" <macrakis at alum.mit.edu>
To: "Richard Hennessy" <rvh2007 at comcast.net>
Cc: "Raymond Toy" <toy.raymond at gmail.com>, "Maxima List" <maxima at math.utexas.edu>
Date: Thu, Jun-26-2008 7:59 AM
Subject: Re: [Maxima] Maxima can't solve this integral equation

I don't think this equation would normally be called an "integral
equation", which generally means an equation where you are solving for
a *function* which appears within the integral. Here you're just
solving for a variable.

Anyway, I'm afraid Maxima's solve routine doesn't even try to solve
for variables within integrals, let alone differential or integral
equations.

             -s