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Math Help - Hard integral

  1. #1
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    Hard integral

    I don't know where to start with the following. None of the methods I try seem to get me very far.

    Show that \int_0^{\frac{\pi}{2}} \frac{1}{3+5\cos{x}}dx = \frac{1}{4}\ln{3}
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  2. #2
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    Hello,
    Quote Originally Posted by pingleby View Post
    I don't know where to start with the following. None of the methods I try seem to get me very far.

    Show that \int_0^{\frac{\pi}{2}} \frac{1}{3+5\cos{x}}dx = \frac{1}{4}\ln{3}
    Use Weierstrass substitution :
    t=\tan \frac x2
    Then \cos x=\frac{1-t^2}{1+t^2}
    And we have dx=\frac{2}{1+t^2} ~dt

    Then you'll get a more friendly integral
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