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    When you integrate a fraction how do you know if it integrates to ln or just normally? (if that makes sense).

    I might be wrong i cant remember but is it just when the power of c is 1 i.e. 1/x would integrate to lnx but 1/x^2 would integrate to -x^-1

    Is that right?
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    (Original post by kiiten)
    When you integrate a fraction how do you know if it integrates to ln or just normally? (if that makes sense).

    I might be wrong i cant remember but is it just when the power of c is 1 i.e. 1/x would integrate to lnx but 1/x^2 would integrate to -x^-1

    Is that right?
    Thats right.

    The rule is \displaystyle \int \dfrac{f'(x)}{f(x)} .dx = \ln | f(x) | +c

    So the requirement is that the numerator is the derivative of the denominator.
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    (Original post by RDKGames)
    Thats right.

    The rule is \displaystyle \int \dfrac{f'(x)}{f(x)} .dx = \ln | f(x) | +c

    So the requirement is that the numerator is the derivative of the denominator.
    Ahh yes i remember now that makes sense, thanks

    So if you had 2x/x^2 the integral would be lnx^2 ?
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    (Original post by kiiten)
    Ahh yes i remember now that makes sense, thanks

    So if you had 2x/x^2 the integral would be lnx^2 ?
    Yes, which is also the same as 2 \ln |x| which coincides with the fact that \dfrac{2x}{x^2}=2 \cdot \dfrac{1}{x}
 
 
 
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