Indefinite Integration
Power Rule
Grade 12
Question:
<p>\(\int x^m x^n - 1 + \frac{1}{x^n} - \frac{mx}{n} + \frac{nx}{m} - \frac{1}{2} - \frac{n}{2m} + \frac{m}{n} dx\) is equal to</p>
<p>(a) \(\frac{m+n}{x^n} + \frac{1}{x} + C\)</p>
<p>(b) \(\frac{m+n}{x^n} + x + C\)</p>
<p>(c) \(\frac{m+n}{x^m + x^n} + C\)</p>
<p>(d) \(-\frac{m+n}{x^m + x^n} + C\)</p>
Step-by-Step Solution
Key Concept: Break the complex expression into simpler terms and apply the power rule for integration to each term.
<p><strong>Solution:</strong> Integrate each term separately according to the power rule for integration.</p>
Correct Answer: A