1. The problem is to solve the integral $$\int x \cos(x) \, dx$$. 2. We use integration by parts formula: $$\int u \, dv = uv - \int v \, du$$. 3. Choose $$u = x$$ so that $$du = dx$$, and $$dv = \cos(x) \, dx$$ so that $$v = \sin(x)$$. 4. Applying the formula: $$\int x \cos(x) \, dx = x \sin(x) - \int \sin(x) \, dx$$. 5. The integral $$\int \sin(x) \, dx = -\cos(x) + C$$. 6. Substitute back: $$x \sin(x) - (-\cos(x)) + C = x \sin(x) + \cos(x) + C$$. 7. Therefore, the solution is $$x \sin(x) + \cos(x) + C$$, which corresponds to option d).