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

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

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

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

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

Solution steps

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

\int \frac{x ^{3}}{x ^{4} - 6} d x

\frac{( 2 s + 3 )}{s ^{2} - 7}

\int sec (2 θ) tan (2 θ) d θ

x \to 5 - lim (\frac{- 1}{x ^{2} - 25})

q \to + (- 11) + lim (ln (q + 11))

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