What is inverse oflaplace 3/((s+2)^2) ?

The answer to inverse oflaplace 3/((s+2)^2) is e^{-2t}*3t

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inverse oflaplace 3/((s+2)^2)

inverse laplace

\frac{3}{( s + 2 ) ^{2}}

e^{- 2 t} \cdot 3 t

Solution steps

L^{- 1} {\frac{3}{( s + 2 ) ^{2}}}

Apply inverse transform rule:

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

then

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

For

\frac{3}{( s + 2 ) ^{2}} : a = - 2, F (s) = \frac{3}{s ^{2}}

= e^{- 2 t} L^{- 1} {\frac{3}{s ^{2}}}

L^{- 1} {\frac{3}{s ^{2}}} : 3 t

= e^{- 2 t} \cdot 3 t

\int \frac{x ^{2} + x}{x ^{3} - x ^{2} - 2 x} d x

\int 5 (3 x - 1) 7 d x

ln (3 - x)

\int \frac{1}{1 + 28 x} d x

\frac{d}{d x} (tan (x) \cdot 107.55)

What is inverse oflaplace 3/((s+2)^2) ?
The answer to inverse oflaplace 3/((s+2)^2) is e^{-2t}*3t