What is inverse oflaplace (2x)/(x^2+2x)+x+5 ?

The answer to inverse oflaplace (2x)/(x^2+2x)+x+5 is Undefined+\delta'(t)+5\delta(t)

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inverse oflaplace (2x)/(x^2+2x)+x+5

inverse laplace

\frac{2 x}{x ^{2} + 2 x} + x + 5

Undefined + δ' (t) + 5 δ (t)

Solution steps

L^{- 1} {\frac{2 x}{x ^{2} + 2 x} + x + 5}

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{2 x}{x ^{2} + 2 x}} + L^{- 1} {x} + L^{- 1} {5}

L^{- 1} {\frac{2 x}{x ^{2} + 2 x}} :

Undefined

L^{- 1} {x} : δ^{'} (t)

L^{- 1} {5} : 5 δ (t)

= Undefined + δ^{^{'}} (t) + 5 δ (t)

x \to 1 lim (x^{\frac{1}{x - 1}})

\frac{d}{d x} (\frac{1}{( 1 + x )})

(1 + 2 x) e^{3 x^{2}}

y^{^{''}} - 14 y^{^{'}} + 48 y = 0

What is inverse oflaplace (2x)/(x^2+2x)+x+5 ?
The answer to inverse oflaplace (2x)/(x^2+2x)+x+5 is Undefined+\delta'(t)+5\delta(t)