What is laplacetransform 2e^t+5 ?

The answer to laplacetransform 2e^t+5 is 2/(s-1)+5/s

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laplacetransform 2e^t+5

laplace transform

2 e^{t} + 5

\frac{2}{s - 1} + \frac{5}{s}

Solution steps

L {2 e^{t} + 5}

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)}

= 2 L {e^{t}} + L {5}

L {e^{t}} : \frac{1}{s - 1}

L {5} : \frac{5}{s}

= 2 \cdot \frac{1}{s - 1} + \frac{5}{s}

Refine

2 \frac{1}{s - 1} + \frac{5}{s} : \frac{2}{s - 1} + \frac{5}{s}

= \frac{2}{s - 1} + \frac{5}{s}

\int 1 + 2 x^{2} + x^{4} d x

\frac{1}{x + 4}, 2

3 e^{\frac{1}{x}}

\int_{0}^{π} sin^{2} (8 x) d x

\int_{- 4}^{4} (3 - x) d x

What is laplacetransform 2e^t+5 ?
The answer to laplacetransform 2e^t+5 is 2/(s-1)+5/s