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Math Help - integrate this?

  1. #1
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    integrate this?

    how would i integrate

     \int \frac{dx}{4x^{2}-4x +17}
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  2. #2
    Super Member
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    Quote Originally Posted by birdman22 View Post
    how would i integrate

     \int \frac{dx}{4x^{2}-4x +17}
    When dealing with a reciprocal quadratic you either need to complete the square or factorise.

    In this case you need to complete the square.

    you should get  \int \frac{dx}{(2x-1)^2 +4^2}

    now use the substitution 2x-1 = 2 \tan u

    give this a shot on your own and see how it goes.

    For checking purposes only, the answer is \frac{1}{8} \arctan \left( \frac{2x - 1 }{4} \right).

    Bobak
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