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I am looking for a technique to solve an indefinite integral of $$ \int \frac{dx}{\sqrt{ax^3+bx^2+cx+f}} $$

I honestly have no idea where to start with this and I cannot find anything like this in an integral table.

Actually I was thinking maybe taylor expand?

Thank you

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    I believe you are out of luck, see http://en.wikipedia.org/wiki/Weierstrass%27s_elliptic_functions#Integral_equation2012-10-09
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    I should add that x is a substitution for 1/r with r being the radial component of the equations of motion for 2D orbits2012-10-09
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    Are you sure you want to solve an indefinite integral of that integral? I suspect that what you actually want to solve is the indefinite integral itself.2012-10-10
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    yes you are correct joriki. I want to just solve that indefinite integral.2012-10-10
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    @Ricardo: There's an edit link underneath the question. If comments lead to a clarification of the question, the question should be updated so that people don't have to read through the comments to understand it.2012-10-10

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