What is inverse oflaplace (4s)/((s+1)^2) ?

The answer to inverse oflaplace (4s)/((s+1)^2) is 4e^{-t}-e^{-t}*4t

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inverse oflaplace (4s)/((s+1)^2)

inverse laplace

\frac{4 s}{( s + 1 ) ^{2}}

4 e^{- t} - e^{- t} \cdot 4 t

Solution steps

L^{- 1} {\frac{4 s}{( s + 1 ) ^{2}}}

Take the partial fraction of

\frac{4 s}{( s + 1 ) ^{2}} : \frac{4}{s + 1} - \frac{4}{( s + 1 ) ^{2}}

= L^{- 1} {\frac{4}{s + 1} - \frac{4}{( s + 1 ) ^{2}}}

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= L^{- 1} {\frac{4}{s + 1}} - L^{- 1} {\frac{4}{( s + 1 ) ^{2}}}

L^{- 1} {\frac{4}{s + 1}} : 4 e^{- t}

L^{- 1} {\frac{4}{( s + 1 ) ^{2}}} : e^{- t} \cdot 4 t

= 4 e^{- t} - e^{- t} \cdot 4 t

\frac{d}{d x} (3 x^{2} + e^{2} x + π^{2})

\int \frac{1}{x ^{2} x ^{2} + 100} d x

f (x) = x^{8} - 9 e^{3 x}

\int_{0}^{π} cos (t) d t

\frac{d}{d x} (2 x^{3} - 12 x^{2} + 18 x)

What is inverse oflaplace (4s)/((s+1)^2) ?
The answer to inverse oflaplace (4s)/((s+1)^2) is 4e^{-t}-e^{-t}*4t