1. **Problem:** Solve the integral $$\int \frac{3x}{x+2} \, dx$$. 2. **Step 1: Simplify the integrand.** Rewrite the fraction by dividing: $$\frac{3x}{x+2} = \frac{3(x+2) - 6}{x+2} = 3 - \frac{6}{x+2}$$ 3. **Step 2: Split the integral.** $$\int \frac{3x}{x+2} \, dx = \int \left(3 - \frac{6}{x+2}\right) dx = \int 3 \, dx - \int \frac{6}{x+2} \, dx$$ 4. **Step 3: Integrate each term.** - $$\int 3 \, dx = 3x + C_1$$ - $$\int \frac{6}{x+2} \, dx = 6 \int \frac{1}{x+2} \, dx = 6 \ln|x+2| + C_2$$ 5. **Step 4: Combine results.** $$3x - 6 \ln|x+2| + C$$ 6. **Answer:** The integral evaluates to $$3x - 6 \ln|x+2| + C$$. This matches option (a).