What is the integral of (2-t)e^{-st} ?

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

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integral of (2-t)e^{-st}

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

x \to 0 lim (\frac{ln ( 1 - 2 x )}{x})

\int \frac{2 u}{1 - u ^{2}} d u

(- 9, 5), (- 3, 3)

\frac{d}{d x} (3^{x - 2})

f (x) = 4 - x, at x = 0

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