`int sinx dx`

Answer

To solve the integral of \( \sin x \, dx \), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Function to Differentiate**: We need to find a function whose derivative is \( \sin x \). We recall that the derivative of \( \cos x \) is \( -\sin x \).

2. **Adjust the Derivative**: Since we want \( \sin x \) and we have \( -\sin x \), we can multiply both sides of the equation by \(-1\). This gives us:
\[ -\frac{d}{dx}(\cos x) = \sin x \]

3. **Integrate**: From the above step, we can conclude that:
\[ \int \sin x \, dx = -\cos x + C \]
where \( C \) is the constant of integration.

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

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