1. **State the problem:** We need to find the indefinite integral $$\int (6e^{2x} + 6x) \, dx$$. 2. **Recall the integration rules:** - The integral of $$e^{ax}$$ with respect to $$x$$ is $$\frac{1}{a}e^{ax} + C$$. - The integral of $$x$$ with respect to $$x$$ is $$\frac{x^2}{2} + C$$. - The integral of a sum is the sum of the integrals. 3. **Apply the integral to each term:** $$\int 6e^{2x} \, dx + \int 6x \, dx$$ 4. **Integrate the first term:** $$6 \int e^{2x} \, dx = 6 \cdot \frac{1}{2} e^{2x} = 3e^{2x}$$ 5. **Integrate the second term:** $$6 \int x \, dx = 6 \cdot \frac{x^2}{2} = 3x^2$$ 6. **Combine the results and add the constant of integration:** $$3e^{2x} + 3x^2 + C$$ **Final answer:** $$\int (6e^{2x} + 6x) \, dx = 3e^{2x} + 3x^2 + C$$