The correct option is (d) \(\frac{7x^3}{3}-\frac{x^4}{4}+x^2+C\)
Explanation: To find \(\int 7x^2-x^3+2x dx\)
\(\int 7x^2-x^3+2x dx=\int 7x^2 dx-\int x^3 dx+2\int x dx\)
Using \(\int x^n dx=\frac{x^{n+1}}{n+1}\), we get
\(\int 7x^2-x^3+2x dx=\frac{7x^{2+1}}{2+1}-\frac{x^{3+1}}{3+1}+2(\frac{x^{1+1}}{1+1})\)
∴\(\int 7x^2-x^3+2x dx=\frac{7x^3}{3}-\frac{x^4}{4}+x^2+C\)