[Maxima] Maxima can't solve this integral equation

[Raymond Toy (RT/EUS)]

Richard Hennessy wrote:
> 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.

FWIW, I think integrate(sqrt(1-z^4),z,-1,1) is 4/3*elliptic_kc(-1).

Ray