Answer
A good first step would be to take out a $\frac{1}{3}$ out of the integral and divide the Integrand's numerator by the denominator.
Work Step by Step
After taking out the $\frac{1}{3}$ and evaluating the Integrand, you get:
$\int \frac{x^{10}-2x^4+10x^2+1}{3x^3 dx}$ = $\frac{1}{3} \int \frac{x^{10}-2x^4+10x^2+1}{x^3} dx$ = $\frac{1}{3} \int (x^7 -2x+\frac{10}{x}+\frac{1}{x^3})dx$, which is easier to integrate.
