What is laplacetransform t^5e^{-t} ?

The answer to laplacetransform t^5e^{-t} is (120)/((s+1)^6)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

laplacetransform t^5e^{-t}

laplace transform

t^{5} e^{- t}

\frac{120}{( s + 1 ) ^{6}}

Solution steps

L {e^{- t} t^{5}}

Use Laplace Transform table:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

For

t^{5} e^{- t} : f (t) = e^{- t}, k = 5

= (- 1)^{5} \frac{d ^{5}}{d s ^{5}} (L {e^{- t}})

L {e^{- t}} : \frac{1}{s + 1}

\frac{d ^{5}}{d s ^{5}} (\frac{1}{s + 1}) = - \frac{120}{( s + 1 ) ^{6}}

= (- 1)^{5} (- \frac{120}{( s + 1 ) ^{6}})

= \frac{120}{( s + 1 ) ^{6}}

x \to 0 - lim (x)

f (x) = x^{2} + 2 x, g (x) = x + 2

\int \frac{2}{x ^{2} - 4} d x

\frac{d}{d t} N = 400 - \frac{900}{( t ^{2} + 2 ) ^{2}}

\frac{d y}{d x} x^{3} + y^{3} = 3 x y

What is laplacetransform t^5e^{-t} ?
The answer to laplacetransform t^5e^{-t} is (120)/((s+1)^6)