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Math Help - Integral

  1. #1
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    Integral

    \int \frac{x\log_e(x)}{\sqrt{x^2-1}} dx

    Any help?

    Thanks
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by usagi_killer View Post
    \int \frac{x\log_e(x)}{\sqrt{x^2-1}} dx ~{\color{red}= I}

    Any help?

    Thanks
    first: use integration by parts with u = \ln x and dv = \frac x{\sqrt{x^2 - 1}}~dx to get

    I = \sqrt{x^2 - 1} \cdot \ln x - \int \frac {\sqrt{x^2 - 1}}x~dx

    Finish off the last integral with a trig sub of x = \sec \theta
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