Monday, September 7, 2015

calculus - Integrating Reciprocals of Polynomials




I have seen integrals of the form 1ax+bdx and 1ax2+bx+cdx
But I cannot see how to integrate reciprocals of higher degree - does there exist a general solution to the integrals of reciprocals of cubics, quartics, and higher?


Answer



Reciprocals of higher degree can have their denominators factored into linear and/or irreducible quadratic terms, and from there, our result can be obtained through partial fraction decomposition.



For more details, see Arturo's excellent answer to this question.


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