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Thread: Need help solving simple integral

  1. #1
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    Need help solving simple integral

    Wolfram Alpha gives an answer of $\displaystyle \frac{1}{2}$, but it doesn't give the steps. Can someone walk me through the problem or a similar problem? I believe I need to use integration by parts but I keep getting stuck.

    Thanks

    $\displaystyle \int_{0}^{\infty}\frac{3x}{(1+x)^{4}}dx$
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  2. #2
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    Re: Need help solving simple integral

    Quote Originally Posted by downthesun01 View Post
    Wolfram Alpha gives an answer of $\displaystyle \frac{1}{2}$, but it doesn't give the steps. Can someone walk me through the problem or a similar problem? I believe I need to use integration by parts but I keep getting stuck.

    Thanks

    $\displaystyle \int_{0}^{\infty}\frac{3x}{(1+x)^{4}}dx$
    try the substitution $\displaystyle u = x+1$
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  3. #3
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    Re: Need help solving simple integral

    Thanks. I just got it myself using integration by parts.

    $\displaystyle u=3x$, $\displaystyle du=3dx $, $\displaystyle dv=\frac{1}{(1+x)^{4}}$, $\displaystyle v\frac{-1}{3(1+x)^{-3}}$
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