If `(d)/(dx) (sin x+c)=cos x`, then find `int cos x dx`.

Answer

To solve the problem, we start with the given equation:

\[ \frac{d}{dx} (\sin x + c) = \cos x \]

We need to find the integral of \(\cos x\) with respect to \(x\).

### Step-by-step Solution:

1. **Understand the given equation**: The equation states that the derivative of \(\sin x + c\) is equal to \(\cos x\). This means that integrating \(\cos x\) will give us \(\sin x + c\).

2. **Integrate both sides**: We can integrate both sides of the equation with respect to \(x\):

\[ \int \cos x \, dx = \int \frac{d}{dx} (\sin x + c) \, dx \]

3. **Apply the Fundamental Theorem of Calculus**: The integral of the derivative of a function returns the function itself (up to a constant). Therefore, we have:

\[ \int \cos x \, dx = \sin x + c \]

4. **Conclusion**: Thus, the integral of \(\cos x\) is:

\[ \int \cos x \, dx = \sin x + C \]

where \(C\) is the constant of integration.

### Final Answer:
\[ \int \cos x \, dx = \sin x + C \]