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Thread: need help with integration

  1. #1
    Feb 2009

    need help with integration

    Int (3x^3.5)/(3+x^2.5) dx

    I tried using integration by parts and the equation uv-int (vdu) and im not getting the right answer. Could someone please show me the steps on how to do this question?
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  2. #2
    Senior Member
    Dec 2007
    Anchorage, AK
    Have you considered making the u-substitution u=\sqrt{x}? Then dx=2u\,du, and your integral becomes

    The first term is easily integrated, leaving the rational function \frac{18u^3}{3+u^5} to be integrated.
    Using the fifth roots of unity, one can factor the denominator above into real linear and quadratic factors:

    One can then use partial fractions to separate the above into rational functions with linear or quadratic denominators, which you should be able to integrate.

    --Kevin C.
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