What is the integral of-1/s e^{-st} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-1/s e^{-st}

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply u-substitution

: \int - \frac{e ^{u}}{s} d u

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{s} (- \frac{1}{s} \cdot \int e^{u} d u)

Use the common integral:

\int e^{u} d u = e^{u}

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

Substitute back

u = - s t

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

Simplify

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

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

Add a constant to the solution

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

\int x (4 x + 5)^{8} d x

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

f (x) = x^{7} - x^{3}

y = sin (\frac{1}{x})

\int sin^{6} (3 x) cos (3 x) d x

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