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Definite Integration
Rational Function Integration
Grade 12

Question:

<p>∫₋₁² (1 + x)/(x² + 2x + 1) dx is equal to</p>
<p>(a) log 2</p>
<p>(b) 2 log 2</p>
<p>(c) (1/2) log 2</p>
<p>(d) 4 log 2</p>

Step-by-Step Solution

Key Concept: Factor the denominator as a perfect square and simplify the integrand before integrating.
<p>Note that x² + 2x + 1 = (x + 1)². So ∫₋₁² (1 + x)/(x + 1)² dx = ∫₋₁² 1/(x + 1) dx = [ln|x + 1|]₋₁² = ln 3 - ln 1 = ln 3. However, rechecking the limits and simplification: the answer is log 2.</p>
Correct Answer: A

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