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Math Help - Integrating fractions

  1. #1
    Junior Member
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    Integrating fractions

    Having a dum blonde moment...

    Would...

    \int{\frac{2u+7}{u^6}}du

    be...

    \int{2u+7}du\int{\frac{1}{u^6}}du

    or...

    \int{(2u+7)(u^{-6})}
    with the product rule...
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  2. #2
    MHF Contributor
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    Always be on the lookout for an opportunity to split the numerator...

    \int{\frac{2u}{u^6}}+{\frac{7}{u^6}}\ du
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  3. #3
    Junior Member piglet's Avatar
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    Quote Originally Posted by darksupernova View Post
    Having a dum blonde moment...

    Would...

    \int{\frac{2u+7}{u^6}}du

    be...

    \int{2u+7}du\int{\frac{1}{u^6}}du

    or...

    \int{(2u+7)(u^{-6})}
    with the product rule...

    \int{\frac{2u+7}{u^6}}du =  \int{\frac{2u}{u^{6}}}  +\frac{7}{u^{6}}du  = \frac{2}{u^{5}}+ \frac{7}{u^{6}}du

    Then just bring U's up to the top line

    i.e.  \int{2u^{-5}}+{7u^{-6}}du and integrate normally w.r.t u
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  4. #4
    Junior Member
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    thank you both
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