I have been trying to solve an integral. I know that the solution exists for the form
$$1- \dfrac{2}{\mathcal{R}^2_{\mathcal{G}}}\int_{0}^{\mathcal{R}_{\mathcal{G}}} \exp (-\Phi r^{\alpha}) r\, {\rm d}r,$$
where $\alpha>0, \mathcal{R}_\mathcal{G}>0$. However, I want to solve
$$1- \dfrac{2}{\mathcal{R}^2_{\mathcal{G}}}\int_{0}^{\mathcal{R}_{\mathcal{G}}} \exp \left(-\Phi \left(\sqrt{r^2+h^2}\right)^{\alpha}\right) r\, {\rm d}r,$$
where $\Phi>0$, $\alpha>0, \mathcal{R}_\mathcal{G}>0 $and $h>0$. Any clue please?