What is the integral of e^{-st}-te^{-st} ?

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

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integral of e^{-st}-te^{-st}

\int e^{- s t} - t e^{- s t} d t

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

Solution steps

\int e^{- s t} - t e^{- s t} d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{- s t} d t - \int e^{- s t} t d t

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

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

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

Add a constant to the solution

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

y = x^{3} - x, y = 3 x

\int_{- \infty}^{0} \frac{1}{5 - 6 x} d x

\int_{1}^{2} \frac{5 - x}{x ^{3}} d x

\frac{d}{d x} ((csc (x))^{2})

n = 1 \sum \infty e^{- 8 n}

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