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Math Help - nightmare integral

  1. #1
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    nightmare integral

    Find the integral.
    1/(x(ln(x))^7)dx
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  2. #2
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    Quote Originally Posted by ArmiAldi View Post
    Find the integral.
    1/(x(ln(x))^7)dx
    just let u=\ln x

    u=\ln x\;du=\frac{dx}{x}

    \int \frac{dx}{x\ln^7 x}=\int \frac{du}{u^7}=-\frac{1}{6u^6}

    Thus, \int \frac{dx}{x\ln^7 x}=-\frac{1}{6\ln^6x}+C
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