I would like to create a program that calculates
$$\int_{x_1}^{x_2}{\frac{dx}{P(x)}}$$ , where $P(x)=ax^3+bx+cx+d$, $a,b,c$ and $d$ are real. I also assume that $P$ is strictly positive on $[x_1,x_2]$.
I had a look at https://en.wikipedia.org/wiki/List_of_integrals_of_rational_functions, but it did not really help me. I feel that the positive condition on $P$ should help to get a closed form formula.