Step 1: Identify the function to integrate, which is (2x + 3).
Step 2: Break down the integral into two parts: ∫(2x) dx and ∫(3) dx.
Step 3: For the first part, ∫(2x) dx, use the power rule: increase the exponent of x by 1 (from 1 to 2) and divide by the new exponent. This gives (2x^2/2).
Step 4: Simplify (2x^2/2) to x^2.
Step 5: For the second part, ∫(3) dx, since 3 is a constant, multiply it by x. This gives 3x.
Step 6: Combine the results from Step 4 and Step 5. You get x^2 + 3x.
Step 7: Add the constant of integration, C, to the result. The final answer is x^2 + 3x + C.
Integration of Polynomials – The question tests the ability to integrate a polynomial function, specifically applying the power rule for integration.
