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Math Help - integration question

  1. #1
    Senior Member
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    Question integration question

    i was wondering about an basic integration technique, the integral of (a+b)^y da and how this may be integrated insede the braket however if the thing inside the braket is not linear e.g.(a^x+b)^y da why it cannot be integrated inside the braket basically and i was wondering how to prove this??
    thanks
    Last edited by hmmmm; December 10th 2008 at 08:54 AM.
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  2. #2
    MHF Contributor
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    Hi - maybe this is of interest -

    " ...integral is non elementary by Chebyshev's theorem. In general,
    the integral of x^p (a + b x^r)^q dx is elementary if and only if
    at least one of (p+1)/r, q, or (p+1)/r + q is an integer
    (see Marchisoto & Zakeri: "An Invitation to Integration in Finite
    Terms", The College Mathematics Journal, Vol. 25, No. 4, Sept.1994,
    pp.295-308).

    Miguel A. Lerma
    8/24/95 " at
    http://www.math.niu.edu/~rusin/known...elementary.int

    Or maybe you just need to notice that 'integrating inside the bracket' would mean following the chain rule for differentiation, and that's why you generally need the x^p in your integrand. But, as seem to notice (here, and before at http://www.mathhelpforum.com/math-he...technique.html) the p will be zero for r = 1.
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