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Thread: What is the best way to integrate this integral ?

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    What is the best way to integrate this integral ?

    Integral $\int_{}^{} (9x^2+6)/(3x^3+6x) dx$

    I understand to use the chain rule but,

    i get ln(3x^3+6x) but the 9x^2+6 has me bit confused....hmm
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    Re: What is the best way to integrate this integral ?

    The numerator is the derivative of the denominator. Whenever the integrand is of the form \frac{f'(x)}{f(x)} you should try the substitution u=f(x).
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    Re: What is the best way to integrate this integral ?

    Quote Originally Posted by bee77 View Post
    Integral $\int_{}^{} (9x^2+6)/(3x^3+6x) dx$
    I understand to use the chain rule but,
    Hi Bee-Bee, learn to use this site.
    Last edited by Plato; Jul 20th 2017 at 04:12 AM.
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    Re: What is the best way to integrate this integral ?

    Quote Originally Posted by Plato View Post
    Hi Bee-Bee, learn to use this site.
    You inadvertently entered "(9x^2+6)/(3x^3+6x^2)" into WolframAlpha, and that was what was last sitting there when I visited it.

    It's really "(9x^2+6)/(3x^3+6x)."



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    Quote Originally Posted by bee77 View Post
    Integral $\int_{}^{} (9x^2+6)/(3x^3+6x) dx$

    I understand to use the chain rule but,

    i get ln(3x^3+6x) but the 9x^2+6 has me bit confused....hmm

    One of the forms of the answer is ln|3x^3 + 6x| + C , or you may see it as log|3x^3 + 6x| + C .

    And, there are still other ways of writing the answer.

    Regardless, it's the logarithm with the base e.

    The graph of the function has a vertical asymptote of x = 0.
    Last edited by greg1313; Jul 20th 2017 at 03:44 PM.
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