Indefinite Integration
Integration by Substitution
Grade 12
Question:
<p>79. \(\int \frac{(1-x^2)^{3/2}}{x^2} dx\) is equal to</p>
<p>(a) \((\sin^{-1} x)^2 + \log(1-x^2) + C\)</p>
<p>(b) \(\frac{\sin^{-1} x}{1-x^2} + \log(1-x^2) + C\)</p>
<p>(c) \(\frac{x \sin^{-1} x}{2} - \log(1-x^2) + C\)</p>
<p>(d) (Not clearly provided in source)</p>
Step-by-Step Solution
Key Concept: Use substitution $x = \sin \theta$ to simplify $(1-x^2)^{3/2}$ and convert to a trigonometric integral.
<p>Solution not provided in the source text.</p>
Correct Answer: A