I'm trying to deal with this article, but I don't understand how equations 5.9 and 5.10 were obtained. I tried to use Mathematica 8 to solve it, but the answer was different. I have a problem with this integral $$ \int _0^{\tau }\int _{\sigma -(\tau -\tau_1)}^{\sigma +(\tau-\tau_1)} \frac{M\ y_0\ \sinh^2(\beta)} {\left(\sigma_1^2+ (\tau_1 \sinh(\beta)+x_0)^2+y_0^2\right)^{3/2}} \ d\sigma_1\ d\tau_1 $$
where $\tau, M, y_0, \beta$ are constants.
I used only a simple Integrate
function with GenerateConditions -> False
.
Maybe I'm doing something wrong in Mathematica. If you know; tell me Mathematica code, please. Otherwise, if there is some kind of algorithm to solve integrals like this, please tell me too.