Find $\int e^x (1 - \cot x + \text{cosec}^2 x) dx$.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $e^x (1 - \cot x) + C$
Let $I=\int e^x (1 - \cot x + \text{cosec}^2 x) dx$
Assume, $f(x) = 1 - \cot x$,
$f'(x) = \text{cosec}^2 x$.
Using the property $\int e^x [f(x) + f'(x)] dx = e^x f(x) + C$:
$I = e^x (1 - \cot x) + C$