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Math Help - Integration

  1. #1
    Member kjchauhan's Avatar
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    Integration

    Pl help me to solve the integral...

    \int \frac{1}{x} e^{-2x} dx

    Thanks in advance
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by kjchauhan View Post
    Pl help me to solve the integral...

    \int \frac{1}{x} e^{-2x} dx

    Thanks in advance
    This integral has no closed form representation as far as I know...
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  3. #3
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    skeeter's Avatar
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    Quote Originally Posted by kjchauhan View Post
    Pl help me to solve the integral...

    \int \frac{1}{x} e^{-2x} dx

    Thanks in advance
    I could be wrong, but I don't think this integral has an elementary, closed-form antiderivative.

    you may have to use a series representation for e^{-2x}.
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  4. #4
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by skeeter View Post
    you may have to use a series representation for e^{-2x}.
    To get started on this, we have

    e^{-2x}=1+(-2x)+\frac{(-2x)^2}{2}+\frac{(-2x)^3}{6}+...

    Divide by x to get \frac{1}{x}+\sum_{n=1}^{\infty}\frac{(-2)^n x^{n-1}}{n!}

    Integrate this term by term (with respect to x).
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