How to solve this integral and is it an application of the Laplace transform?

36 Views Asked by At

I have an integral that has no apparent solution: $$\int _0^le^{-\sqrt{\left(p_x+xr_x\right)^2+\left(p_y+xr_y\right)^2}}dx$$ I reduced it down to a simpler integral that still has no obvious solution: $$\int _a^be^{-sx}\cdot \frac{1}{\sqrt{1-\frac{r^2}{x^2}}}dx$$ My question is if this integral can be solved using the Laplace Transform and if so, how?