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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.

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Sarah

  1. 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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    Steve

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