I'm looking for a solution to $$\int x^{-a} \Gamma\left( b, c x^{-d} \right) dx.$$
Mathematica gives me the following solution, but I'd like to know/understand the steps involved in finding it.
$$\int x^{-a} \Gamma\left( b, c x^{-d} \right) dx = \frac{x^{1-a} \left(\left(c x^{-d}\right)^{\frac{1-a}{d}} \Gamma \left(\frac{a+b d-1}{d},c x^{-d}\right)-\Gamma \left(b,c x^{-d}\right)\right)}{a-1}.$$
The following solution, to a similar integral, seems to be a starting point. However, I have no idea how to proceed from that.
https://functions.wolfram.com/GammaBetaErf/Gamma2/21/01/02/01/
Does someone know how to find this solution?