Question

∴\[\int e^{2x} \left( - \sin x + 2 \cos x \right) dx\]

Answer 1

\[\text{ Let I } = \int e^{2x} \left( - \sin x + 2\cos x \right)dx\]

\[\text{ Put  e}^{2x} \cos x = t\]

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

\[\left[ 2 e^{2x} \cos x + e^{2x} \times \left( - \sin x \right) \right]dx = dt\]

`  ∴   \text{ I } = \int   dt `

\[ = t + C\]

\[ = e^{2x} \cos x + C\]