I am trying to find an analytical solution for this problem:
$ \int_{-a/2}^{a/2}\frac{z}{z^{2}+(x-x')^{2}}\frac{sx'-y}{\sqrt{z^{2}+(x-x')^{2}+\left(sx'-y\right)^{2}}}dx' $
where $x$, $y$, $z$, $a$ and $s$ are constants (all real). and I can't figure out the way to do it. I tried the following change of variable without success:
$x' = x + \tan u \sqrt{\left(sx'-y\right)^2 + z^2}$
can you please help with the change of variable, or the solution to the indefinite integral (if my approach is not on the right track) so that I can calculate the above. Thanks.
Mathematica gives a complicated results for
$\int \frac{z}{z^{2}+(x-t)^{2}} \frac{st-y} {z^{2}+(x-t)^{2}+(st-y)^{2}} dt$
and $\int_{-\frac{a}{2}}^{\frac{a}{2}} \frac{z}{z^{2}+(x-t)^{2}} \frac{st-y} {z^{2}+(x-t)^{2}+(st-y)^{2}} dt$