Indefinite Integration
Inverse Trigonometric Functions
Grade 12
Question:
<p>\(\int \frac{dx}{(2x - 7)\sqrt{x^2 - 7x + 12}}\) is equal to</p>
<p>(A) \(2\sec^{-1}(2x - 7) + c\)</p>
<p>(B) \(\sec^{-1}(2x - 7) + c\)</p>
<p>(C) \(\frac{1}{2}\sec^{-1}(2x - 7) + 2\)</p>
<p>(D) None of these</p>
Step-by-Step Solution
Key Concept: Recognize the standard form of inverse secant integral and manipulate the integrand accordingly.
<p>This integral requires substitution and standard inverse trigonometric integral form.</p>
Correct Answer: B