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I trying to evaluate the following integral

$$\int_0^\infty \dfrac { x^{m-1} \Gamma(A,\mathcal B x^q)} {\left[1+(\eta x)^n\right]^p} \,\mathrm dx$$

where the integration is w.r.t. $x$, and the other parameters are real positive.

Any idea?

FYI: with some change of variable, the following integral might be simpler to evaluate:

$$\int_0^\infty \dfrac {z^{\widetilde{m}-1} \Gamma(A,z)} {\left[ 1+(\tilde \eta z)^{\widetilde n} \right]^p} \,\mathrm dz$$

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