12.26 Find the function $F(x)$, the graph of which passes through the point $M_{0}(3 ;-2)$, given that $F^{\prime}(x)=4 x^{2}+9 x^{-2}$.

Calculate the integrals (12.27-12.30):
12.26 We have $F(x)=4 \frac{x^{3}}{3}+9 \frac{x^{-1}}{-1}+C$. Substituting the coordinates of the point $M_{0}(3 ;-2)$ into this equation, we get $-2=\frac{4}{3} 3^{3}-9 \cdot 3^{-1}+C$, from which $C=-35$.

Answer: $F(x)=\frac{4}{3} x^{3}-\frac{9}{x}-35$.