1. The problem is to find the integral of $\sin(2x + y)$ with respect to $x$. 2. The integral formula for $\sin(ax + b)$ with respect to $x$ is: $$\int \sin(ax + b) \, dx = -\frac{1}{a} \cos(ax + b) + C$$ where $a$ and $b$ are constants, and $C$ is the constant of integration. 3. In this problem, $a = 2$ and $b = y$ (treated as a constant with respect to $x$). 4. Applying the formula: $$\int \sin(2x + y) \, dx = -\frac{1}{2} \cos(2x + y) + C$$ 5. Explanation: Since $y$ is constant with respect to $x$, we treat $2x + y$ as a linear function in $x$. The integral of sine of a linear function is the negative cosine of that function divided by the coefficient of $x$. Final answer: $$\boxed{-\frac{1}{2} \cos(2x + y) + C}$$