Step 1: Identify the function to integrate, which is (2x + 3).
Step 2: Break 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 (2/2)x^2 = x^2.
Step 4: For the second part, ∫(3) dx, since 3 is a constant, multiply it by x. This gives 3x.
Step 5: Combine the results from Step 3 and Step 4: x^2 + 3x.
Step 6: Add the constant of integration, C, to the final result: x^2 + 3x + C.
Integration of Polynomials – The question tests the ability to integrate a polynomial function, specifically applying the power rule for integration.
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