# Thread: How to integrate this?

1. ## 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. Originally Posted by charliechuckiechuckles
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.