1. The problem is to evaluate the integral $$\int x^3 \sin x + y^n \, du$$. 2. Since the integral is with respect to $u$, and the integrand contains $x^3 \sin x + y^n$ which are constants with respect to $u$, we use the rule: $$\int c \, du = cu + C$$ where $c$ is a constant with respect to $u$. 3. Here, $c = x^3 \sin x + y^n$, so the integral becomes: $$\int (x^3 \sin x + y^n) \, du = (x^3 \sin x + y^n) u + C$$ 4. This is the final answer since $x$ and $y$ are treated as constants with respect to $u$. Therefore, the solution is: $$(x^3 \sin x + y^n) u + C$$