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Question
\[\int e^x \left( 1 - \cot x + \cot^2 x \right) dx =\]
Options
ex cot x + C
−ex cot x + C
ex cosec x + C
−ex cosec x + C
MCQ
Solution
−ex cot x + C
\[\text{Let }I = \int e^x \left( 1 - \cot x + \cot^2 x \right)dx\]
\[ = \int e^x \left( {cosec}^2 x - \cot x \right)dx\]
\[\text{As we know that }\int e\left\{ f\left( x \right) + f' {}^x \left( x \right) \right\} = e^x f\left( x \right) + C\]
\[ \therefore I = - e^x \cot x + C\]
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