Calculate the integral ∫ (x^2 + 2x + 1)/(x + 1) dx.

Calculate the integral ∫ (x^2 + 2x + 1)/(x + 1) dx.

Step 1: Start with the integral ∫ (x^2 + 2x + 1)/(x + 1) dx.
Step 2: Simplify the integrand (the expression inside the integral).
Step 3: Notice that (x^2 + 2x + 1) can be factored as (x + 1)(x + 1).
Step 4: Rewrite the integrand as ((x + 1)(x + 1))/(x + 1).
Step 5: Cancel the (x + 1) in the numerator and denominator, leaving you with x + 1.
Step 6: Now, the integral simplifies to ∫ (x + 1) dx.
Step 7: Integrate (x + 1) to find the antiderivative: ∫ (x + 1) dx = (1/2)x^2 + x + C.
Step 8: Write down the final answer: (1/2)x^2 + x + C.

Polynomial Long Division – The question tests the ability to simplify a rational function by performing polynomial long division before integrating.
Basic Integration – The question assesses knowledge of basic integration techniques for polynomials.