What is inverse oflaplace (e^{-s})/((s+1)^2) ?

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

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inverse oflaplace (e^{-s})/((s+1)^2)

inverse laplace

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

H (t - 1) e^{- t + 1} (t - 1)

Solution steps

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

Apply inverse transform rule:

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

then

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

Where

H (t)

is Heaviside step function

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

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

= H (t - 1) e^{- (t - 1)} (t - 1)

= H (t - 1) e^{- t + 1} (t - 1)

\int - e^{- x} x d x

\int_{0}^{10} f (x) d x

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\int p + 4 d p

\int x^{3} (2 - x^{2})^{12} d x

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