1. The problem is to find the indefinite integral of $\cos\left(\frac{x}{3}\right)$ with respect to $x$. 2. Recall the formula for integrating cosine of a linear function: $$\int \cos(ax) \, dx = \frac{1}{a} \sin(ax) + C$$ where $a$ is a constant and $C$ is the constant of integration. 3. Here, $a = \frac{1}{3}$, so applying the formula: $$\int \cos\left(\frac{x}{3}\right) dx = 3 \sin\left(\frac{x}{3}\right) + C$$ 4. Explanation: Since the argument of cosine is $\frac{x}{3}$, the derivative of $\sin\left(\frac{x}{3}\right)$ is $\frac{1}{3} \cos\left(\frac{x}{3}\right)$, so to compensate, we multiply by 3. 5. Final answer: $$\boxed{3 \sin\left(\frac{x}{3}\right) + C}$$