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Math Help - S x ( e ^ [SQRT[X]] - e ^ -3 * x^2) * dx

  1. #1
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    S x ( e ^ [SQRT[X]] - e ^ -3 * x^2) * dx

    Here is my problem:
    S x ( e ^ [SQRT[X]] - e ^ -3 * x^2) * dx . I have tried to call all my friends, but no one knew :/
    S x ( e ^ [SQRT[X]]  -  e ^ -3 * x^2) * dx-thkk001.jpg
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    You made the right thing when you split the integral into two.

    Alright,

    \int xe^{x^2}dx=\frac{e^{x^2}}{2}+C

    Now to the first integral:

    \int{xe^{\sqrt{x}}dx

    First... substitute \sqrt{x}=t and you will get:

    2\int {e^t}{ t^3}dt

    Now you can do integration by part 3 times... or:

    Find the coefficients of:

    \int {e^t}{ t^3}dt=Ae^t {t^3}+Be^t {t^2}+Ce^t {t}+De^t

    (by differentiation)
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