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Math Help - Evalute The Following Integral. (1)

  1. #1
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    Evalute The Following Integral. (1)

    Hello
    here is it :
    \int \frac{ x e^x }{ \sqrt{e^x+1} }dx.

    by parts would be an idea.
    but it really hard to apply the integration by parts directly.

    any ideas??
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by TWiX View Post
    Hello
    here is it :
    \int \frac{ x e^x }{ \sqrt{e^x+1} }dx.

    by parts would be an idea.
    but it really hard to apply the integration by parts directly.

    any ideas??
    \ln(z)=x then \sqrt{z+1}=m
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  3. #3
    Super Member General's Avatar
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    Quote Originally Posted by TWiX View Post
    Hello
    here is it :
    \int \frac{ x e^x }{ \sqrt{e^x+1} }dx.

    by parts would be an idea.
    but it really hard to apply the integration by parts directly.

    any ideas??
    use x=ln(t) to get:

    \int \frac{ln(t)}{\sqrt{t+1}}dt.

    use t+1=w^2 to get:

    2\int ln(w^2-1) dw = 2\int ln(w+1) dw + 2 \int ln(w-1) dw.

    two quick "by parts" will kill it.
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