Evaluate $\int \frac{(1 + \cos x)}{x + \sin x} dx$.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\ln|x + \sin x| + C$
Consider that,
$I = \int \frac{(1 + \cos x)}{(x + \sin x)} dx$
Let $x + \sin x = t \Rightarrow (1 + \cos x) dx = dt$
$∴I = \int \frac{1}{t} dt = \log |t| + C$
$= \log |(x + \sin x)| + C$