Evaluate the integral of (2x + 1) dx from 0 to 3

Problem: Evaluate the definite integral $\int_{0}^{3} (2x + 1) \, dx$.

Steps

1. Find the antiderivative
   $$\left[ x^2 + x \right]_{0}^{3}$$
2. Substitute the upper limit of integration
   $$(3^2 + 3)$$
3. Simplify the upper limit expression
   $$9 + 3 = 12$$
4. Substitute the lower limit of integration
   $$(0^2 + 0) = 0$$
5. Subtract the lower limit value from the upper limit value
   $$12 - 0$$