The problem is to evaluate the indefinite integral of $3x^{-4}$.

1. Problem Description

The problem is to evaluate the indefinite integral of $3x^{-4}$.

2. Solution Steps

We need to find the integral of $3x^{-4}$ with respect to $x$. We can use the power rule for integration, which states that $\int x^n dx = \frac{x^{n+1}}{n+1} + C$, where $n \neq -1$ and $C$ is the constant of integration.

In this case, we have:

$\int 3x^{-4} dx = 3 \int x^{-4} dx$

Using the power rule, we get:

$3 \int x^{-4} dx = 3 \cdot \frac{x^{-4+1}}{-4+1} + C = 3 \cdot \frac{x^{-3}}{-3} + C = -x^{-3} + C = -\frac{1}{x^3} + C$

3. Final Answer

The indefinite integral of $3x^{-4}$ is $-\frac{1}{x^3} + C$. Therefore, the correct answer is C.

Final Answer: C