Indefinite Integration
Trigonometric Integrals
Premium Question
Grade 12
Question:
$\int \frac{dx}{1 + \sin x}$ equals:
(1) $\tan x - \sec x + C$
(2) $\tan x + \sec x + C$
(3) $\sec x - \tan x + C$
(4) $-\tan x - \sec x + C$
Step-by-Step Solution
Key Concept: Multiply numerator and denominator by $(1 - \sin x)$ and use $1 - \sin^2 x = \cos^2 x$ to rewrite the integrand in terms of $\sec^2 x$ and $\sec x \tan x$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)