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Question
\[\int e^x \left( \cos x - \sin x \right) dx\]
Sum
Solution
\[\text{ Let I } = \int e^x \left( \cos x - \sin x \right) dx \]
\[\text{ let e}^x \cos x = t \]
\[\text{ Diff both sides w . r . t x}\]
\[ e^x \cdot \cos x + e^x \left( - \sin x \right) = \frac{dt}{dx} \text{ Put e}^x f\left( x \right) = t\]
\[ \Rightarrow e^x \left( \cos x - \sin x \right) dx = dt\]
\[ \therefore \int e^x \left( \cos x - \sin x \right) dx = \int dt\]
\[ \Rightarrow I = t + C\]
\[ = e^x \cos x + C\]
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