What function solves the differential equation f'(x)=3x^2 y=-6x^3+C y=6x^3+C y=6x+C y=x^3+C y=-x^3+C

## Step 1: Integrate both sides<br />### To solve the differential equation $f'(x) = 3x^2$, we need to integrate both sides of the equation with respect to $x$. This reverses the differentiation process.<br />## Step 2: Apply the power rule of integration<br />### The power rule of integration states that $\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$, where $n \neq -1$ and $C$ is the constant of integration. Applying this rule to our integral, we get $\int 3x^2 \, dx = 3 \cdot \frac{x^{2+1}}{2+1} + C = 3 \cdot \frac{x^3}{3} + C = x^3 + C$.