Is there a way to solve the following integral completely?

int(int(x^2+y^2, y = -sqrt(2*a*x-x^2) .. sqrt(2*a*x-x^2)), x = 0 .. 2*a)

When I try solving that all I get is the following:

All is well when I calculate it using polar coordinates though:

int(int(r^3, r = 0 .. 2*a*cos(t)), t = -(1/2)*Pi .. (1/2)*Pi)

=         

Why doesn't maple solve the first one completely and is there a way around this?

Thanks

Calor

EDIT:EDIT: I found what I was looking for. Thanks!

eq:=(V^(1-r/(r-s))*V*k/(r-2*s)+_C1)*V^(r/(r-s))=0;

solve(eq,C1);

Can anyone tell me why nothing happens when I solve the above equation for C1.

I've been coming across this problem a few times lately, but sometimes when the equations are less complicated it does work from time to time. 

Any help would be greatly appreciated.

EDIT:  Thanks Markiyan Hirnyk. 

But I'm still having some trouble.

f:=t->(-r*t+s*t+V)^(r/(r-s));

eq2:=diff(C*f(t),t)+C*f(t)*r/(V+s*t-r*t)=s*k*t;

solve(eq2,C);

When I try solving eq2 nothing happens. 

This time C is just a variable I used and not one Maple generated.

So why doesn't it work with this particular equation?