Indefinite Integration
Trigonometric Functions
Grade 12
Question:
<p>Evaluate \(\int \frac{\sin 2x}{\sin^4 x} dx\)</p>
<p>(A) \(\frac{4}{5}C - \cot^{7/2} x\)</p>
<p>(B) \(\frac{4}{5}C - \cot^{5} x\)</p>
<p>(C) \(\frac{4}{5}C - \cot^{5} x\)</p>
<p>(D) None of these</p>
Step-by-Step Solution
Key Concept: Recognize that $\sin 2x = 2\sin x \cos x$ and use cotangent substitution for efficient integration.
<p>Use the substitution $u = \cot x$ to convert this trigonometric integral into a polynomial form.</p>
Correct Answer: C