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Step-by-step Solution

Integrate $e^{-x}\left(1-x\right)$ from $1$ to $\infty $

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asin
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Answer

$-\frac{71}{193}$

Step-by-step explanation

Problem to solve:

$\int_1^{\infty}\left(e^{-x}\left(1-x\right)\right)dx$
1

Multiplying polynomials $e^{-x}$ and $1+-x$

$\int_{1}^{\infty }\left(e^{-x}-e^{-x}x\right)dx$
2

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int_{1}^{\infty } e^{-x}dx+\int_{1}^{\infty }-e^{-x}xdx$

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Answer

$-\frac{71}{193}$
$\int_1^{\infty}\left(e^{-x}\left(1-x\right)\right)dx$

Main topic:

Definite integrals

Related formulas:

5. See formulas

Time to solve it:

~ 0.17 seconds