1. **State the problem:** We need to evaluate the integral $$\int t \cos x \, dx$$. 2. **Identify variables:** Here, $t$ is treated as a constant with respect to $x$ because the integration is with respect to $x$. 3. **Recall the integral formula:** The integral of $\cos x$ with respect to $x$ is $\sin x + C$. 4. **Apply the constant multiple rule:** Since $t$ is constant, it can be factored out of the integral: $$\int t \cos x \, dx = t \int \cos x \, dx$$ 5. **Integrate:** Using the formula, $$t \int \cos x \, dx = t (\sin x + C) = t \sin x + C$$ 6. **Final answer:** $$\boxed{t \sin x + C}$$ This is the antiderivative of $t \cos x$ with respect to $x$.