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Math Help - Substitution Indefinite Integral Problem

  1. #1
    Junior Member
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    Mar 2009
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    61

    Exclamation Substitution Indefinite Integral Problem

    Not sure what to do after i get down to the step i'm at, if its all correct so far.

    \int (\frac{x^2+2}{x^3+6x+3})dx

    u=x^3+6x+3

    du=3x^2+6 dx

    du=3(x^2+2)

    (x^2+2)dx=\frac{du}{3}

    Not sure about or after this:

    \int (\frac{\frac{1}{3}du}{u})
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  2. #2
    Member
    Joined
    Dec 2008
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    Auckland, New Zealand
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    You don't need substitution...

    \int \frac{x^2+2}{x^3+6x+3}~dx = \frac{1}{3} \int \frac{3x^2+6}{x^3+6x+3}~dx

    Now remember the rule \int \frac{f'(x)}{f{x}}~dx = \ln{|f(x)|} ?

    But the last integral you mentioned with "u" will give you the correct answer once you integrate and substitute back. It uses the same rule I mentioned above.
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