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Math Help - help with integration

  1. #1
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    help with integration

    I need help with the following integral:

    \int_{0}^{\infty}\frac{x}{(x+1)^{n+2}}, where n \in \mathbb{N}

    Do I need complex integration for this?
    Last edited by mr fantastic; September 4th 2009 at 02:02 PM. Reason: Fixed latex
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  2. #2
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    Put u = x + 1. Then x = u - 1 and du = dx:

     \int_0^{\infty} \frac{x }{(x+1)^{n+2}} dx = \int_1^{\infty} \frac{u-1}{u^{n+2}} du = \int_1^{\infty} \frac{1}{u^{n+1}} du - \int_1^{\infty} \frac{1}{u^{n+2}} du .

    Does this help?
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  3. #3
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    I've solved it using that method and got \frac{1}{n(n+1)}, but it looks like I have to solve it by complex integration.

    Could you please help me out?
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  4. #4
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    Complex integration is beyond my scope. Hopefully a more knowledgeable user will help you out soon. Sorry.
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  5. #5
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    Quote Originally Posted by trelee View Post
    I've solved it using that method and got \frac{1}{n(n+1)}, but it looks like I have to solve it by complex integration.

    Could you please help me out?
    What have you tried and where are you stuck? Have you thought about:

    1. What contour to use?

    2. What function to use?
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