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  4. The value of ∫ e2x(2sin 3x + 3cos 3x)dx is

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Q. The value of $\int e^{2x}\left(2sin 3x + 3cos 3x\right)dx$ is

Integrals

Solution:

$\int e^{2x} \left(2 sin 3x + 3 cos 3x\right)dx$

$=2\int e^{2x} sin 3x dx + 3 \int e^{2x} cos 3x dx$

$= e^{2x} sin 3x - 3 \int e^{2x} cos 3x dx +3\int e^{2x} cos 3x dx +C$

$=e^{2x}sin3x+ C$