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

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

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

inverse laplace

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

2 e^{- t} sin (2 t)

Solution steps

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

Expand

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

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

Use the constant multiplication property of Inverse Laplace Transform:

For function

f (t)

and constant

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

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

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

= 2 e^{- t} \frac{1}{2} sin (2 t)

Refine

2 e^{- t} \frac{1}{2} sin (2 t) : 2 e^{- t} sin (2 t)

= 2 e^{- t} sin (2 t)

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

\int \frac{x ^{3}}{( 1 + 5 x ^{2} ) ^{3}} d x

\int 4 x^{2} 3 x^{3} + 2 d x

\frac{d}{d x} (\frac{15 x ^{6}}{3 x})

n = 0 \sum \infty \frac{1}{n ^{0.5}}

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