What is inverse oflaplace 3/((2s^2+8s+10)) ?

The answer to inverse oflaplace 3/((2s^2+8s+10)) is 3/2 e^{-2t}sin(t)

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inverse oflaplace 3/((2s^2+8s+10))

inverse laplace

\frac{3}{( 2 s ^{2} + 8 s + 10 )}

\frac{3}{2} e^{- 2 t} sin (t)

Solution steps

L^{- 1} {\frac{3}{( 2 s ^{2} + 8 s + 10 )}}

Expand

\frac{3}{2 s ^{2} + 8 s + 10} : \frac{3}{2} \cdot \frac{1}{( s + 2 ) ^{2} + 1}

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

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)}

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

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

= \frac{3}{2} e^{- 2 t} sin (t)

\int \frac{1}{x ^{2} - 8 x + 1} d x

\int \frac{e ^{y}}{y} d y

\int 22 x^{2} ln (x) d x

g (x) = x^{2}

x \to 0 lim (I n (1 + sin (x)))

What is inverse oflaplace 3/((2s^2+8s+10)) ?
The answer to inverse oflaplace 3/((2s^2+8s+10)) is 3/2 e^{-2t}sin(t)