Question:
Evaluate the following integrals:
$\int e^{-2 x} \sin x d x$
Solution:
Let $I=\int e^{-2 x} \sin x d x$
We know that, $\int \mathrm{e}^{\operatorname{ax}} \sin b x d x=\frac{e^{\operatorname{ax}}}{a^{2}+b^{2}}\{a \sin b x-b \cos b x\}+c$
$=\frac{e^{-2 x}}{5}\{-2 \sin x-\cos x\}+c$
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