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Math Help - How to integrate this?

  1. #1
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    How to integrate this?

    I don't know where to begin with integrating this equation. It is number 1 on the page the link brings you to and is the one with the natural log not the tangent. Again, I need to integrate this even further than is already, unfortunately. Any help would be greatly apreciated.

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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by charliechuckiechuckles View Post
    I don't know where to begin with integrating this equation. It is number 1 on the page the link brings you to and is the one with the natural log not the tangent. Again, I need to integrate this even further than is already, unfortunately. Any help would be greatly apreciated.

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    Ok, so I suppose you know that to get the arctan antiderivative you would use completing the square.

    For the log antiderivative, you would begin thusly: recall that the roots of the quadratic are \displaystyle x = \frac {-b \pm \sqrt{b^2 - 4ac}}{2a}, so the integral can be written as

    \displaystyle \int \frac 1{\left(x - \frac {-b + \sqrt{b^2 - 4ac}}{2a} \right) \left(x - \frac {-b - \sqrt{b^2 - 4ac}}{2a} \right)}~dx

    Now, proceed via partial fractions decomposition.
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