Answer
$$\frac{{{x^9}}}{9} - \frac{{3{x^4}}}{4} + x + C$$
Work Step by Step
$$\eqalign{
& {\text{Find }}\int {\left( {{x^8} - 3{x^3} + 1} \right)dx} \cr
& {\text{use }}\int {{x^n}} dx = \frac{{{x^{n + 1}}}}{{n + 1}} + C \cr
& = \frac{{{x^{8 + 1}}}}{{8 + 1}} - \frac{{3{x^{3 + 1}}}}{{3 + 1}} + x + C \cr
& {\text{Simplify}} \cr
& = \frac{{{x^9}}}{9} - \frac{{3{x^4}}}{4} + x + C \cr} $$
