# closed-form solution to $\int_0^\infty x^a\exp(-bx)\left(\frac{1}{\text{erfc}(c\sqrt{x})}\right)^{2a}$

This integral comes up in a problem in Statistics involving power laws. Here are some notes if anyone is interested. The integral in question would be related to equation (7) therein.

I would like to compute $$\int_0^\infty x^a\exp(-bx)\left(\frac{1}{\text{erfc}(c\sqrt{x})}\right)^{2a} dx,$$ where $$b > 0$$, $$a >0$$ and $$c \in \mathbb{R}$$ and erfc is the complementary error function.

This looks hopeless. Anything I could try to squeeze out a closed-form solution?