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Math Help - Tricky integral

  1. #1
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    Tricky integral

    { 4/[x sqrt(x^2 - 4)] dx







    The answer is 2 arcsec (x/2) but can anyone show me the steps to in solving it? I tried partial decomposition and some trig substitution but nothing really worked.
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  2. #2
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    Quote Originally Posted by Kaitosan View Post
    { 4/[x sqrt(x^2 - 4)] dx







    The answer is 2 arcsec (x/2) but can anyone show me the steps to in solving it? I tried partial decomposition and some trig substitution but nothing really worked.
    Let x = 2 \sec \theta so dx = 2 \sec \theta \tan \theta d \theta

    and the integral becomes

     \int \frac{4 \cdot 2 \sec \theta \tan \theta }{2 \sec \theta \;2 \tan \theta} d \theta = 2 \int d \theta

    integrate and use your substitution to get your answer
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    OOH I see. I was confused because I wasn't used to substituting any "x" outside trigonometric expressions. Thanks.
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