Indefinite Integration
Trigonometric Integrals
Grade 12
Question:
<p>The value of $\displaystyle \int \frac{secx(2+secx)}{(1+2secx)^2} dx$ is equal to</p>
<p>(A) $\frac{sinx}{2+cosx} + c$</p>
<p>(B) $\frac{cosx}{2+cosx} + c$</p>
<p>(C) $\frac{sinx}{2+sinx} + c$</p>
<p>(D) $-\frac{cosx}{2+sinx} + c$</p>
Step-by-Step Solution
Key Concept: Decompose the integrand using algebraic manipulation and recognize standard trigonometric integral forms
<p>This integral involves trigonometric functions and requires careful algebraic simplification before integration.</p>
Correct Answer: B