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Step-by-step Solution

Solve the trigonometric integral $\int e^{-x}\sin\left(x\right)dx$

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e
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ln
log
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lim
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sin
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asin
acos
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asinh
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Answer

$-\frac{1}{2}\cos\left(x\right)e^{-x}-\frac{1}{2}\sin\left(x\right)e^{-x}+C_0$

Step-by-step explanation

Problem to solve:

$\int e^{\left(-1\right)\cdot x}\sin\left(x\right)dx$
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Use the integration by parts theorem to calculate the integral $\int e^{-x}\sin\left(x\right)dx$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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Answer

$-\frac{1}{2}\cos\left(x\right)e^{-x}-\frac{1}{2}\sin\left(x\right)e^{-x}+C_0$

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