What is inverse oflaplace (-(16))/((5(x^2+8x+25))) ?

The answer to inverse oflaplace (-(16))/((5(x^2+8x+25))) is -16/15 e^{-4t}sin(3t)

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inverse oflaplace (-(16))/((5(x^2+8x+25)))

inverse laplace

\frac{- ( 16 )}{( 5 ( x ^{2} + 8 x + 25 ) )}

- \frac{16}{15} e^{- 4 t} sin (3 t)

Solution steps

L^{- 1} {\frac{- ( 16 )}{( 5 ( x ^{2} + 8 x + 25 ) )}}

Expand

\frac{- 16}{5 ( x ^{2} + 8 x + 25 )} : - \frac{16}{5} \cdot \frac{1}{( x + 4 ) ^{2} + 9}

= L^{- 1} {- \frac{16}{5} \cdot \frac{1}{( x + 4 ) ^{2} + 9}}

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{16}{5} L^{- 1} {\frac{1}{( x + 4 ) ^{2} + 9}}

L^{- 1} {\frac{1}{( x + 4 ) ^{2} + 9}} : e^{- 4 t} \frac{1}{3} sin (3 t)

= - \frac{16}{5} e^{- 4 t} \frac{1}{3} sin (3 t)

Refine

- \frac{16}{5} e^{- 4 t} \frac{1}{3} sin (3 t) : - \frac{16}{15} e^{- 4 t} sin (3 t)

= - \frac{16}{15} e^{- 4 t} sin (3 t)

\int \frac{2}{cos ( x )} d x

\int_{- 2}^{c o s (x)} 3 t d t

\int x (2 x + 3) d x

(3) (0.4)

x \to - 1 - lim (\frac{x + 1}{∣ x + 1 ∣})

What is inverse oflaplace (-(16))/((5(x^2+8x+25))) ?
The answer to inverse oflaplace (-(16))/((5(x^2+8x+25))) is -16/15 e^{-4t}sin(3t)