What is laplacetransform 45(1-e^{-625x}) ?

The answer to laplacetransform 45(1-e^{-625x}) is (45)/s-(45)/(s+625)

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laplacetransform 45(1-e^{-625x})

laplace transform

45 (1 - e^{- 625 x})

\frac{45}{s} - \frac{45}{s + 625}

Solution steps

L {45 (- e^{- 625 x} + 1)}

Expand

45 (1 - e^{- 625 x}) : 45 - 45 e^{- 625 x}

= L {45 - 45 e^{- 625 x}}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {45} - 45 L {e^{- 625 x}}

L {45} : \frac{45}{s}

L {e^{- 625 x}} : \frac{1}{s + 625}

= \frac{45}{s} - 45 \cdot \frac{1}{s + 625}

Refine

\frac{45}{s} - 45 \frac{1}{s + 625} : \frac{45}{s} - \frac{45}{s + 625}

= \frac{45}{s} - \frac{45}{s + 625}

f (x) = \frac{1}{1 + x ^{2}}, (2, \frac{2}{5})

\frac{d}{d x} (x^{2} (3 x - 4)^{3})

\int_{0}^{1} x^{2} e^{x} d x

y = \frac{16}{x ^{2} - 6 x - 55}, y = 0, x = - 3, x = 3

What is laplacetransform 45(1-e^{-625x}) ?
The answer to laplacetransform 45(1-e^{-625x}) is (45)/s-(45)/(s+625)