integrate(asinh(x/sqrt(z^2+y^2)), y) -> could be improved

Many thanks to all the participants in the thread, and it would be great if
my question would result in an improvement in maxima.

If so, i would like to mention a second point where maxima could be
improved:

integrate(asinh(x/sqrt(z^2+y^2)), y);

x*'integrate(y^2/((z^2+y^2+x^2)*%e^(log(z^2+y^2+x^2)/2)+x*z^2+x*y^2+x^3\
),y)+(2*y*log(sqrt(z^2+y^2+x^2)+x)-y*log(z^2+y^2))/2+(2*z^2+2*x^2)*atan(y/sqrt\
(z^2+x^2))/(2*sqrt(z^2+x^2))-atan(y/z)*z

this results contains an %e^log(x), but even after taking that away, maxima
still doesn't want to integrate it (and the ratsimp(),algrabraic didn't work
here). The integral is possible though (it's essentially the same as the
function I started this thread with).

=======================================
If anyone is interested, here's what I'm using maxima for:

To calculate the potential around a plane with constant charge-density, one
needs to integrate the following function to x and to y:

    p(x,y,z) = 1/sqrt(x^2+y^2+z^2)

Integrating to x gives with maxima: asinh(x/sqrt(z^2+y^2)),
and with Wolfram: log(x+sqrt(x^2+y^2+z^2)).

Both answers are correct (they differ just a constant value), but when I ask
maxima to then integrate asinh(x/sqrt(z^2+y^2)) to y, it fails to do so, as
mentioned above. Giving maxima the result from Wolfram results in the
incorrect result I started this thread with.