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Math Help - Hard Integration help

  1. #1
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    Hard Integration help

    Can you please solve this problems?

    \int\frac{x^4-x {dx}}{x^2-1}
    \int\frac{e^{4y}}{e^{2y}+1}dy
    \int\frac{dx}{(2x-1)[3-2 \ln (1-2x)]}
    \int\frac{dx}{x(1-x^3)}
    \int\frac{(3-4x)x dx}{\sqrt[3]{1-x}}


    Thanks in Advance
    Last edited by mr fantastic; August 3rd 2009 at 04:25 AM. Reason: Fixed exponents in second integral
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  2. #2
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    Quote Originally Posted by Yuroichi View Post
    Can you please solve this problems?

    \int\frac{x^4-x {dx}}{x^2-1}
    \int\frac{e^{4y}}{e^{2y}+1}dy
    \int\frac{dx}{(2x-1)[3-2 \ln (1-2x)]}
    \int\frac{dx}{x(1-x^3)}
    \int\frac{(3-4x)x dx}{\sqrt[3]{1-x}}


    Thanks in Advance
    1. Note that \frac{x^4-x}{x^2-1} = \frac{x(x - 1)(x^2 + x + 1)}{(x - 1)(x + 1)} = \frac{x^3 + x^2 + x}{x + 1} = x^2 + 1 - \frac{1}{x + 1}.

    2. Start by substituting u = e^{2y}.

    3. Start by substituting u = \ln (1 - 2x).

    4. Completely factorise the denominator and then use a partial fraction decomposition.

    5. Start by substituting u^3 = 1 - x.

    If you need more help, please post your working and state where you get stuck.
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