integral of Fractional function

Question

What is the solution to this integral? This integral is attached in the equation below.

\begin{eqnarray*} \int \frac{dx}{Ax^n+Bx+c} \end{eqnarray*}

Answer 1

If the polynomial $A x^n + B x + c$ has $n$ distinct complex roots $r_1, \ldots, r_n$, then the integral can be written as $$ \sum_{j=1}^n \dfrac{\ln(x - r_j)}{n A r_j^{n-1} + B} + \text{constant}$$