Answer
$$\int e^{-5x}sin\,x\,dx=-\frac{e^{-5x}}{26}(cos\,x+5sin\,x)+C$$
Work Step by Step
$$\int e^{-5x}sin\,x\,dx=-e^{-5x}cos\,x-5e^{-5x}sin\,x-25\int e^{-5x}sin\,x\,dx$$
$$26\int e^{-5x}sin\,x\,dx=-e^{-5x}cos\,x-5e^{-5x}sin\,x$$
$$\int e^{-5x}sin\,x\,dx=-\frac{e^{-5x}}{26}(cos\,x+5sin\,x)+C$$
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