What is inverse oflaplace 1/((s-2)^6) ?

The answer to inverse oflaplace 1/((s-2)^6) is (e^{2t}t^5)/(120)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inverse oflaplace 1/((s-2)^6)

inverse laplace

\frac{1}{( s - 2 ) ^{6}}

\frac{e ^{2 t} t ^{5}}{120}

Solution steps

L^{- 1} {\frac{1}{( s - 2 ) ^{6}}}

Apply inverse transform rule:

L^{- 1} {F (s)} = f (t)

then

L^{- 1} {F (s - a)} = e^{a t} f (t)

For

\frac{1}{( s - 2 ) ^{6}} : a = 2, F (s) = \frac{1}{s ^{6}}

= e^{2 t} L^{- 1} {\frac{1}{s ^{6}}}

L^{- 1} {\frac{1}{s ^{6}}} : \frac{t ^{5}}{120}

= \frac{e ^{2 t} t ^{5}}{120}

\frac{d}{d x} (x^{2} + 2 x + 5)

x \to 0 + lim (\frac{1}{x ^{5}})

\int \frac{x}{1 - x ^{4}} d x

\int (\frac{cos ( x )}{x}) d x

\int \frac{25}{x ^{2}} d x

What is inverse oflaplace 1/((s-2)^6) ?
The answer to inverse oflaplace 1/((s-2)^6) is (e^{2t}t^5)/(120)