The value of int {{e^{2x}}(2sin 3x + 3cos 3x) | vedclass

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(A) We use the standard integration formula: $\int {{e^{ax}}[af(x) + f'(x)]\,dx = {e^{ax}}f(x) + C}$.Here,$a = 2$ and $f(x) = \sin 3x$.Then,$f'(x) = \

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${e^{2x}}\sin 3x + C$

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(A) We use the standard integration formula: $\int {{e^{ax}}[af(x) + f'(x)]\,dx = {e^{ax}}f(x) + C}$.Here,$a = 2$ and $f(x) = \sin 3x$.Then,$f'(x) = \frac{d}{dx}(\sin 3x) = 3\cos 3x$.The given integral is $\int {{e^{2x}}(2\sin 3x + 3\cos 3x)\,dx}$.Comparing this with the formula,we have $f(x) = \sin 3x$ and $f'(x) = 3\cos 3x$.Therefore,the integral is equal to ${e^{2x}}\sin 3x + C$.

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

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