Indefinite Integration
Integration by Substitution
Grade 12
Question:
<p>\(\int \frac{x+1}{(x^2+1)^{3/2}} dx\) equals</p>
<p>(A) \(\sec^{-1}x - \frac{\ln x}{x+1} + C\)</p>
<p>(B) \(\sec^{-1}x + \frac{\ln x}{2(x+1)} + C\)</p>
<p>(C) \(\cos^{-1}x - \frac{\ln x}{2(x+1)} + C\)</p>
<p>(D) None of these</p>
Step-by-Step Solution
Key Concept: Use substitution or rationalization techniques to simplify the denominator and integrate.
<p>This is an indefinite integral requiring substitution and algebraic manipulation to evaluate.</p>
Correct Answer: A