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Thread: Integral

  1. #1
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Feb 2008
    Yuma, AZ, USA


    Quote Originally Posted by navynukejones
    Thanks for the help man with the last problem, the book I am using isn't very clear on how to do some of these. I have one more that is similar to that one that I cant figure out it is: integrate: 5x^2-x+11/(x^2+4)(x-1).
    use partial fractions to get

    $\displaystyle \int \frac{5x^2-x+11}{(x^2+4)(x-1)}dx=\int \left( \frac{2x+1}{x^2+4}+\frac{3}{x-1}\right)dx=$

    now we use termise division of the first term to get

    $\displaystyle \int \left( \frac{2x}{x^2+4}+\frac{1}{x^2+4}+\frac{3}{x-1}\right)dx=\ln|x^2+4|+\frac{1}{2}\tan^{-1}(x/2)+3\ln|x-1|+C$
    Last edited by TheEmptySet; Apr 23rd 2008 at 06:04 PM.
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