To evaluate the indefinite integral of 3x² with respect to x.

The problem asks to evaluate the indefinite integral of $3x^2$ with respect to $x$.

$$\int 3x^2 dx$$

The constant multiple rule states that $\int c \cdot f(x) dx = c \int f(x) dx$. Here, $c=3$ and $f(x)=x^2$.

$$\int 3x^2 dx = 3 \int x^2 dx$$

The power rule for integration states that $\int x^n dx = \frac{x^{n+1}}{n+1} + C$, where $n \neq -1$. Here, $n=2$.

$$3 \int x^2 dx = 3 \left( \frac{x^{2+1}}{2+1} \right) + C$$ $$= 3 \left( \frac{x^3}{3} \right) + C$$

$$= \frac{3x^3}{3} + C$$ $$= x^3 + C$$

The final answer is $x^3 + C$.