What is inverse oflaplace 3/(4(s+1)^2-16) ?

The answer to inverse oflaplace 3/(4(s+1)^2-16) is 3/16 e^t-3/16 e^{-3t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inverse oflaplace 3/(4(s+1)^2-16)

inverse laplace

\frac{3}{4 ( s + 1 ) ^{2} - 16}

\frac{3}{16} e^{t} - \frac{3}{16} e^{- 3 t}

Solution steps

L^{- 1} {\frac{3}{4 ( s + 1 ) ^{2} - 16}}

Take the partial fraction of

\frac{3}{4 ( s + 1 ) ^{2} - 16} : \frac{3}{16 ( s - 1 )} - \frac{3}{16 ( s + 3 )}

= L^{- 1} {\frac{3}{16 ( s - 1 )} - \frac{3}{16 ( s + 3 )}}

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{3}{16 ( s - 1 )}} - L^{- 1} {\frac{3}{16 ( s + 3 )}}

L^{- 1} {\frac{3}{16 ( s - 1 )}} : \frac{3}{16} e^{t}

L^{- 1} {\frac{3}{16 ( s + 3 )}} : \frac{3}{16} e^{- 3 t}

= \frac{3}{16} e^{t} - \frac{3}{16} e^{- 3 t}

\int_{0}^{8} 400 - 20 t d t

\int x^{3} ln (4 x) d x

\int sinh (x) d x

\frac{d}{d x} (arcsin (\frac{1}{x ^{2} + 4}))

\int 1 + x^{\frac{4}{5}} d x

What is inverse oflaplace 3/(4(s+1)^2-16) ?
The answer to inverse oflaplace 3/(4(s+1)^2-16) is 3/16 e^t-3/16 e^{-3t}