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Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...

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Integration of a particular rational expression [closed]

I am trying to solve the following integration, where $a,b,c,d,e$ and $f$ are constants: $$I=\int\frac{x^4+ax^3+bx^2+cx+d}{x^3(x^3+ex+f)}dx$$ I tried to solve the integral using the following two methods … QUESTION: Is it possible to solve the integration analytically using any other suitable method? If no such methods are possible, do there exist any approximation technique that might work? …