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Find $\int e^x (1 - \cot x + \text{cosec}^2 x) dx$. |
$e^x (\cot x - 1) + C$ $e^x (1 - \cot x) + C$ $e^x (1 + \text{cosec}^2 x) + C$ $e^x (1 + \cot x) + C$ |
$e^x (1 - \cot x) + C$ |
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 $\int e^x [f(x) + f'(x)] dx = e^x f(x) + C$: $I = e^x (1 - \cot x) + C$ |
