Question

Solve the integral:

$\int \frac{x^4+x^2+1}{x^2-x+1}dx$

Answer 1

$\begin{array}{c}I=\int \frac{x^4+x^2+1}{x^2-x+1}dx\\ I=\int \left(x^2+x+1\right)dx\\ I=\frac{x^3}{3}+\frac{x^2}{2}+x+C\end{array}$