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How do integrate this with respect to x?

integral of ((x^y)/y!)e^(-2x) from 0 to infinity

The e is an exponential. The answer is supposed to be (1/2)^(y+1) but I don't know the steps to getting it.

1 answer

Must be some special form. I tried an online integrator, and got

(1/2)^(y+1) Γ(y+1)/y!

But since Γ(y+1) = y!, that gives your answer.

I'd suggest looking into integral forms involving the gamma function.
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