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Question
\[\int e^x \left( \cot x - {cosec}^2 x \right) dx\]
Sum
Solution
\[\text{ Let I }= \int e^x \left( \cot x - {cosec}^2 x \right)dx\]
\[\text{ here f(x) } = \text{ cot x put e}^x f(x) = t\]
\[ f'(x) = - {cosec}^2 x\]
\[\text{ let e}^x \cot x = t\]
\[\text{ Diff both sides w . r . t x }\]
\[ e^x \cot x + e^x \left( - {cosec}^2 x \right) = \frac{dt}{dx}\]
\[ \Rightarrow e^x \left( \cot x - {cosec}^2 x \right)dx = dt\]
\[ \therefore \int e^x \left( \cot x - {cosec}^2 x \right)dx = \int dt\]
\[ = t + C\]
\[ = e^x \cot x + C\]
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