Indefinite Integration
Trigonometric Integrals
JEE Main 2017
Grade 12
Question:
$\int \frac{\cos 2x}{(\cos x + \sin x)^2} \, dx$ equals:
(1) $\ln |\sin x + \cos x| + C$
(2) $-\ln |\sin x + \cos x| + C$
(3) $\ln |\sin x - \cos x| + C$
(4) $\sin x + \cos x + C$
Step-by-Step Solution
Key Concept: Factor $\cos 2x = (\cos x - \sin x)(\cos x + \sin x)$, cancel one factor with the denominator, and substitute $t = \sin x + \cos x$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)