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I cannot integrate $\int_a^{\infty} x e^{-(x-a)} dx$. I know the answer should be $(a+1)$ but when I use integration by parts I do not get that answer. Note that $a$ is a constant.

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    Now that the post is modified, the answer is $(a+1)$.2012-04-28

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$\int x e^{-(x-a)} = e^a\int xe^{-x}$

$\int xe^{-x} = -xe^{-x} - \int -e^{-x} +c= -e^{-x}(x+1) +c$ (applying Integration by parts)

so the final answer is, $-e^{a-x}(x+1) +c.e^{a}$

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    lord12: Then you can copy the answer above, with this modification in mind, and see what happens.2012-04-28