Question

\[\int e^x \left( \cos x - \sin x \right) dx\]

Answer 1

\[\text{  Let I } = \int e^x \left( \cos x - \sin x \right) dx \]

\[\text{ let e}^x \cos x = t \]

\[\text{  Diff both  sides  w . r . t x}\]

\[ e^x \cdot \cos x + e^x \left( - \sin x \right) = \frac{dt}{dx} \text{ Put e}^x f\left( x \right) = t\]

\[ \Rightarrow e^x \left( \cos x - \sin x \right) dx = dt\]

\[ \therefore \int e^x \left( \cos x - \sin x \right) dx = \int dt\]

\[ \Rightarrow I = t + C\]

\[ = e^x \cos x + C\]