What is the integral of e^{-sx}(2-x) ?

The integral of e^{-sx}(2-x) is -e^{-sx} 1/s (2-x)+e^{-sx} 1/(s^2)+C

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integral of e^{-sx}(2-x)

\int e^{- s x} (2 - x) d x

- e^{- s x} \frac{1}{s} (2 - x) + e^{- s x} \frac{1}{s ^{2}} + C

Solution steps

\int e^{- s x} (2 - x) d x

Apply Integration By Parts

: - e^{- s x} \frac{1}{s} (2 - x) - \int e^{- s x} \frac{1}{s} d x

= - e^{- s x} \frac{1}{s} (2 - x) - \int e^{- s x} \frac{1}{s} d x

\int e^{- s x} \frac{1}{s} d x = - e^{- s x} \frac{1}{s ^{2}}

= - e^{- s x} \frac{1}{s} (2 - x) - (- e^{- s x} \frac{1}{s ^{2}})

Simplify

= - e^{- s x} \frac{1}{s} (2 - x) + e^{- s x} \frac{1}{s ^{2}}

Add a constant to the solution

= - e^{- s x} \frac{1}{s} (2 - x) + e^{- s x} \frac{1}{s ^{2}} + C

x \to 1 lim (\frac{1}{x ^{3} - 1})

\frac{d}{d x} (3 - 3 cos (x))

\frac{d y}{d x} = (x - 4) e^{- 2 y}

y^{^{'}} = 6 x^{2} \cdot y

\int 4 e^{- 7 x} d x

What is the integral of e^{-sx}(2-x) ?
The integral of e^{-sx}(2-x) is -e^{-sx} 1/s (2-x)+e^{-sx} 1/(s^2)+C