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Popular >

inverse oflaplace x/(x+8)

Solution

inverse laplace

\frac{x}{x + 8}

Solution

δ (t) - 8 e^{- 8 t}

Solution steps

L^{- 1} {\frac{x}{x + 8}}

Take the partial fraction of

\frac{x}{x + 8} : 1 - \frac{8}{x + 8}

= L^{- 1} {1 - \frac{8}{x + 8}}

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} {1} - L^{- 1} {\frac{8}{x + 8}}

L^{- 1} {1} : δ (t)

L^{- 1} {\frac{8}{x + 8}} : 8 e^{- 8 t}

= δ (t) - 8 e^{- 8 t}

Popular Examples

integral of (cos(x))/x

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

tangent of 5x^2-7x tangent of

5 x^{2} - 7 x

derivative of a*x*e^{bx}

\frac{d}{d x} (a \cdot x \cdot e^{b x})

integral of (y-1)/(-y-1)

\int \frac{y - 1}{- y - 1} d y

(\partial)/(\partial y)(2(y+1)e^{2x})

\frac{\partial}{\partial y} (2 (y + 1) e^{2 x})

Frequently Asked Questions (FAQ)

What is inverse oflaplace x/(x+8) ?
The answer to inverse oflaplace x/(x+8) is \delta(t)-8e^{-8t}