What is laplacetransform 6e^{-5t}+5t ?

The answer to laplacetransform 6e^{-5t}+5t is 6/(s+5)+5/(s^2)

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laplacetransform 6e^{-5t}+5t

laplace transform

6 e^{- 5 t} + 5 t

\frac{6}{s + 5} + \frac{5}{s ^{2}}

Solution steps

L {6 e^{- 5 t} + 5 t}

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)}

= 6 L {e^{- 5 t}} + 5 L {t}

L {e^{- 5 t}} : \frac{1}{s + 5}

L {t} : \frac{1}{s ^{2}}

= 6 \cdot \frac{1}{s + 5} + 5 \cdot \frac{1}{s ^{2}}

Refine

6 \frac{1}{s + 5} + 5 \frac{1}{s ^{2}} : \frac{6}{s + 5} + \frac{5}{s ^{2}}

= \frac{6}{s + 5} + \frac{5}{s ^{2}}

What is laplacetransform 6e^{-5t}+5t ?
The answer to laplacetransform 6e^{-5t}+5t is 6/(s+5)+5/(s^2)