1. The problem is to find the integral of $\sinh x$ with respect to $x$, given as $\int \sinh x \, dx$. The statement also shows the result $\cosh x + C$, where $C$ is the constant of integration. 2. Recall the definitions and derivatives of hyperbolic functions: - $\frac{d}{dx} \sinh x = \cosh x$ - $\frac{d}{dx} \cosh x = \sinh x$ 3. To find $\int \sinh x \, dx$, we look for a function whose derivative is $\sinh x$. 4. Since $\frac{d}{dx} \cosh x = \sinh x$, it follows that: $$\int \sinh x \, dx = \cosh x + C$$ where $C$ is the constant of integration. 5. The horizontal double-headed arrow above the integral symbol indicates the integral is taken over the entire real line or is an indefinite integral, confirming the result includes the constant $C$. 6. Therefore, the integral of $\sinh x$ is $\cosh x + C$. This completes the solution.