On Fri, 2011-02-18 at 09:05 +0100, leon.magiera at wp.pl wrote:
> Given:
> assume(a>0,b>0);
> ex:(1-y/b)/(x^2+y^2+z0^2)^(3/2);
> integrate(integrate(ex,y,-b,b),x,-a,a);
>
> Is this integration to hard?
Hi,
to investigate why Maxima is failing, let's include a partial fraction
expansion before the x integration is done:
(%i1) display2d:false$
(%i2) assume(a>0,b>0,notequal(z0,0));
(%o2) [a > 0,b > 0,notequal(z0,0)]
(%i3) ex: (1-y/b)/(x^2+y^2+z0^2)^(3/2)$
(%i4) integrate( ex,y,-b,b );
(%o4) 2*b*sqrt(z0^2+x^2+b^2)/(z0^4+(2*x^2+b^2)*z0^2+x^4
+b^2*x^2)
(%i5) partfrac( %,x );
(%o5) 2*sqrt(z0^2+x^2+b^2)/(b*(z0^2+x^2))
-2/(b*sqrt(z0^2+x^2+b^2))
(%i6) integrate( %, x);
(%o6) 2*('integrate(sqrt(z0^2+x^2+b^2)/(z0^2+x^2),x))/b
-2*asinh(x/sqrt(z0^2+b^2))/b
The second fraction was integrated, but we were left with an integral of
the type:
(%i5) integrate( sqrt(x^2+4)/(x^2+1), x );
(%o5) 'integrate(sqrt(x^2+4)/(x^2+1),x)
which seems easy, but it is not. Maxima does not have any method to find
that integral.
Regards,
Jaime