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Math Help - Integration Problem....answer check???

  1. #1
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    Integration Problem....answer check???

    Here is the question



    This is my attempt. Is this correct?
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  2. #2
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    Correct .
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  3. #3
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    Correct.

    You could have also used the substitution u = x+3:

    \displaystyle \blacktriangleright 3\int\frac{r^2}{r+3}\;{dr} = \int\frac{(u-3)^2}{u}\;{du}
    \displaystyle = 3\int\frac{u^2-6u+9}{u}\;{du} = 3\int{\frac{9}{u}+u-6\;{du}
    \displaystyle = 27\ln{u}-\frac{3}{2}u^2-18u+k = 27\ln(r+3)-\frac{3}{2}(r+3)^2-18(r+3)+k
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  4. #4
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    ^^^
    Its r not x.
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  5. #5
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    Thanks. But the correct answer include abs sign between ln.
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