What is inverse oflaplace 5/((s-3)^4) ?

The answer to inverse oflaplace 5/((s-3)^4) is (5e^{3t}t^3)/6

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inverse oflaplace 5/((s-3)^4)

inverse laplace

\frac{5}{( s - 3 ) ^{4}}

\frac{5 e ^{3 t} t ^{3}}{6}

Solution steps

L^{- 1} {\frac{5}{( s - 3 ) ^{4}}}

Apply inverse transform rule:

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

then

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

For

\frac{5}{( s - 3 ) ^{4}} : a = 3, F (s) = \frac{5}{s ^{4}}

= e^{3 t} L^{- 1} {\frac{5}{s ^{4}}}

L^{- 1} {\frac{5}{s ^{4}}} : \frac{5 t ^{3}}{6}

= \frac{5 e ^{3 t} t ^{3}}{6}

2 x^{3}, 18 x

x \to 8 lim (7 x + ∣ x - 8 ∣)

\int \frac{ln ( 1 + x ^{2} )}{x ^{2}} d x

\int \frac{x}{( x y + 1 ) ^{2}} d y

2 y^{^{''}} + 20 y^{^{'}} + 50 y = 0

What is inverse oflaplace 5/((s-3)^4) ?
The answer to inverse oflaplace 5/((s-3)^4) is (5e^{3t}t^3)/6