What is inverse oflaplace (s+3)/((s+1)^2) ?

The answer to inverse oflaplace (s+3)/((s+1)^2) is e^{-t}+e^{-t}*2t

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inverse oflaplace (s+3)/((s+1)^2)

inverse laplace

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

e^{- t} + e^{- t} \cdot 2 t

Solution steps

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

Take the partial fraction of

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

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

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

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

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

\frac{d y}{d t} = - 4 (y - 2)

\frac{d}{d y} (6 y)

y = ln (\frac{a + b x}{a - b x})

cos (x + 1)

\frac{\partial}{\partial x} (12 y^{5} x^{3} + 35 y^{8} x^{6})

What is inverse oflaplace (s+3)/((s+1)^2) ?
The answer to inverse oflaplace (s+3)/((s+1)^2) is e^{-t}+e^{-t}*2t