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Math Help - Integration by change of variable

  1. #1
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    Integration by change of variable

    \int \frac{-x}{(x+1)-\sqrt (x+1)} dx

    Kind of lost, I tried letting u=x+1, then follow through, but my answer does not match up with the right answer

    the square root goes over the entire quantity x+1

    thanks
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  2. #2
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    make the u substitution u=\sqrt{x+1}. Then x=u^2-1, and dx=2u\,du. When you make this subtitution, factor the numerator and the denominator (they're both polynomials) and cancel common factors. The result is easily integrable.
    --Kevin C.
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  3. #3
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    Your sub will work fine.

    Let u=x+1, \;\ du=dx, \;\ u-1=x

    Make the subs and you get:

    \frac{1-u}{u-\sqrt{u}}=\frac{-1}{\sqrt{u}}-1

    Now integrate that. Easier, huh?.
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  4. #4
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    Quote Originally Posted by doctorgk View Post
    \int \frac{-x}{(x+1)-\sqrt (x+1)} dx

    Kind of lost, I tried letting u=x+1, then follow through, but my answer does not match up with the right answer

    the square root goes over the entire quantity x+1

    thanks
    You can also make the substitution u^2=x+1, you would end up integrating -2\int u+1\:du
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