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Math Help - natural exponential integral

  1. #1
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    natural exponential integral

    \int e^{-\sqrt{x}}

    Surely, this must be on this forum somewhere?
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  2. #2
    Eater of Worlds
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    You could use integration by parts.

    Let u=e^{-\sqrt{x}}, \;\ dv=dx, \;\ v=x, \;\ du=\frac{-1}{2e^{\sqrt{x}}\sqrt{x}}dx
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  3. #3
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    here goes.

    u = \sqrt x

    du = \frac {1}{2} \frac {1}{ \sqrt x} dx

    du = \frac {1}{2} \frac {1}{u} dx

    dx = 2u du

    so we get

    2 \int u e^{-u} du<br />

    use integration by parts, to finish this off.

    I get  -2 \sqrt x e^{-\sqrt x} -  2 e^{-\sqrt x } + C
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