Indefinite Integration
Rational Functions
Grade 12
Question:
<p>If \(I = \int \frac{x^2 - 1}{x^3(2x^4 - 2x^2 + 1)} dx\) is equal to:</p>
<p>(a) \(\frac{2x^4 - 2x^2 + 1}{x^2} + C\)</p>
<p>(b) \(\frac{2x^4 - 2x^2 + 1}{x} + C\)</p>
<p>(c) \(\frac{2x^4 - 2x^2 + 1}{x} + C\)</p>
<p>(d) \(\frac{2x^4 - 2x^2 + 1}{2x^2} + C\)</p>
Step-by-Step Solution
Key Concept: Look for relationships between numerator and the derivative of denominator to apply the fundamental integration pattern.
<p>Use substitution or recognize that the numerator is related to the derivative of the denominator. Differentiate the options to verify.</p>
Correct Answer: A