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Math Help - Evaluate the integral

  1. #1
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    Evaluate the integral

    Evaluate the integral :

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  2. #2
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    Hi

    Spoiler:

    \int \frac{dx}{x(1+x^{2009})} = \int \left(\frac{1}{x}-\frac{x^{2008}}{1+x^{2009}}\right) \: dx = \ln x - \frac{\ln(1+x^{2009})}{2009}
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  3. #3
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    Quote Originally Posted by simplependulum View Post

    Evaluate the integral : \int \frac{dx}{x(1 + x^{2009})}.
    let \alpha > 0 and put x = \frac{1}{t}. then we get \int \frac {dx}{x(1 + x^{\alpha})} = - \int \frac {t^{\alpha - 1}}{1+t^{\alpha}} \ dt = - \frac{1}{\alpha} \ln |1 + t^{\alpha}| + c=-\frac{1}{\alpha} \ln |1 + x^{-\alpha}| + c.
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  4. #4
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    Yes . It isn't difficult actually

    but I was shocked and scared when my friend gave me this integral because the degree is too large 2009 I had no confidence to solve at that time
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