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integration where numerator is equal to differentiation of denominator Watch

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    Hi guys,
    can anyone explain to me the best way you can integrate a function where numerator is equal to differentiation of denominator ? actually on the example blow i somehow made a mistake along the way but can't spot it so i keep getting wrong answer
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    (Original post by Alen.m)
    Hi guys,
    can anyone explain to me the best way you can integrate a function where numerator is equal to differentiation of denominator ? actually on the example blow i somehow made a mistake along the way but can't spot it so i keep getting wrong answer
    \displaystyle \int \frac{g'(x)}{g(x)} dx

    sub, \displaystyle u=g(x)

    so the integral becomes, \displaystyle \int \frac{1}{u} du


    You should be able to complete it from there.
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    You can just take it as a fact that
     \displaystyle \int \frac{f'(x)}{f(x)} dx = \ln |f(x)| +c .
    I suggest that you prove it yourself starting off with y=ln(f(x)) and finding dy/dx (implicit differentiation). It may help the result make more sense.
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    thanks guys
 
 
 
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