1. The problem is to find the integral of $\cos x$ with respect to $x$. 2. The formula for the integral of cosine is: $$\int \cos x \, dx = \sin x + C$$ where $C$ is the constant of integration. 3. Explanation: The derivative of $\sin x$ is $\cos x$, so integrating $\cos x$ returns $\sin x$ plus a constant. 4. Therefore, the solution is: $$\int \cos x \, dx = \sin x + C$$ This is the final answer.