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Math Help - Non-Trivial Definite Integral with Exponential

  1. #1
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    Non-Trivial Definite Integral with Exponential

    Hi,

    Does someone how to solve the integral

    Int^(+ Infinity)_(- Infinity) dx (x e^( -x/2) ) / (1 + a x^2 e^(- x) )

    a is an arbitrary constant.
    The integral runs from - Infinity to + Infinity.

    I tried solving it with substitution, but it doesnt seem to work.

    Regards
    Abdullah
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by abdullah View Post
    Hi,

    Does someone how to solve the integral

    Int^(+ Infinity)_(- Infinity) dx (x e^( -x/2) ) / (1 + a x^2 e^(- x) )

    a is an arbitrary constant.
    The integral runs from - Infinity to + Infinity.

    I tried solving it with substitution, but it doesnt seem to work.

    Regards
    Abdullah
    There is no closed form for the indefinite integral, so I'd say this one is ripe for contour integration.

    -Dan
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