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Math Help - Need help evaluating indefinate integral.

  1. #1
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    Need help evaluating indefinate integral.

    int [x/(x+1)^(1/2)]
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  2. #2
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    Quote Originally Posted by saykhong View Post
    int [x/(x+1)^(1/2)]
    \int\frac{x}{\sqrt{x+1}}\;{dx}. Letting u = \sqrt{x+1} gives {2}\int\frac{u(u^2-1)}{u}\;{du} = {2}\int\left(u^2-1\right)\;{du} = ...
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  3. #3
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    You could also let u = x + 1 then

    \displaystyle  \int \dfrac{(u-1)^2}{\sqrt{u}}du  expand and integrate.
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  4. #4
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    \displaystyle\int{\frac{x}{\sqrt{x+1}}\,dx}=\int{\  sqrt{x+1}\,dx}-\int{\frac{dx}{\sqrt{x+1}}}=\frac{2}{3}{{(x+1)}^{\  frac{3}{2}}}-2\sqrt{x+1}+k.
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