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Math Help - Integral partial fractions

  1. #1
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    Integral partial fractions

    Evaluate the following indenite integral,

    ∫(x^3-5x) / (x^3-2x^2+4x-8)

    The answer i get is:

    x+9/2 log(x^2+4)-9/4 arctan(x/2) - 1/4 log |x-2| + C

    I was wondering if anyone could help confirm if this is correct or not.

    Kind regards.
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  2. #2
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    Re: Integral partial fractions

    Quote Originally Posted by tylersmith7690 View Post
    Evaluate the following indenite integral,
    ∫(x^3-5x) / (x^3-2x^2+4x-8)
    The answer i get is:
    x+9/2 log(x^2+4)-9/4 arctan(x/2) - 1/4 log |x-2| + C
    I was wondering if anyone could help confirm if this is correct or not.
    Here is a web-check.
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  3. #3
    MHF Contributor

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    Re: Integral partial fractions

    Yes, that looks good to me.
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  4. #4
    Junior Member FelixFelicis28's Avatar
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    Re: Integral partial fractions

    Quote Originally Posted by tylersmith7690 View Post
    Evaluate the following indenite integral,

    ∫(x^3-5x) / (x^3-2x^2+4x-8)

    The answer i get is:

    x+9/2 log(x^2+4)-9/4 arctan(x/2) - 1/4 log |x-2| + C

    I was wondering if anyone could help confirm if this is correct or not.

    Kind regards.
    I've just sat down and done it now - unless I'm mistaken, you're out by a factor of 1/4 on the \ln (x^2 + 4) part but the rest looks good to me.
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