What is laplacetransform 5te^{-5t} ?

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

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laplacetransform 5te^{-5t}

laplace transform

5 t e^{- 5 t}

\frac{5}{( s + 5 ) ^{2}}

Solution steps

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

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

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

L {t e^{- 5 t}} : \frac{1}{( s + 5 ) ^{2}}

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

Refine

5 \frac{1}{( s + 5 ) ^{2}} : \frac{5}{( s + 5 ) ^{2}}

= \frac{5}{( s + 5 ) ^{2}}

\int \frac{7 x ^{2} - 1}{x ^{2}} d x

f (x) = \frac{1}{x}, at x = 1

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

\frac{d}{d x} (5 x^{2} + 3 x)

\int \frac{x + 5}{x ^{2} + x - 2} d x

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