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Thread: Integral of exponential of complicated argument

  1. #1
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    Integral of exponential of complicated argument

    Hi, I need help to solve the following integral.
    $\displaystyle \int_{-\infty}^{\infty} \int_{-\infty}^{x} y \exp[-(y-cx-a)^2] \exp[-(x-b)^2] dy dx $
    Last edited by sur23; Jul 1st 2010 at 06:58 AM.
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  2. #2
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    The first integral is of the form $\displaystyle \int_{-\infty}^x ye^{-(y- A)^2}dy$ with A= (cx+a). If you let $\displaystyle u= y-A$, then du= dy and the integral becomes $\displaystyle \int_{-\infty}^{(1-c)x-a}(u+ A)e^{-u^2}du= \int_{-infty}^{(1-c)x-a} ue^{-u^2}du- A\int_{-\infty}^{(1-c)x-a}e^{-u^2}du$ which cannot be done in terms of elementary functions.
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