How to solve the following integral

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Can I ask how to solve the following integral

$$\int_{0}^{\infty} \frac{e^{-Ay}}{y^{B} \left( Cy + D \right)}dy$$

where $A, B, C$ and $D$ are positive constants.

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$$ \int_0^{+\infty} \frac{e^{-A y}}{y^B (C y + D)}{\rm d}y = C^{B-1} D^{-B} \Gamma (1-B) e^{\frac{A D}{C}} \Gamma \left(B,\frac{A D}{C}\right), ~~0 < B < 1 $$

Good luck!