What is laplacetransform 3te^{-2t} ?

The answer to laplacetransform 3te^{-2t} is 3/((s+2)^2)

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laplacetransform 3te^{-2t}

laplace transform

3 t e^{- 2 t}

\frac{3}{( s + 2 ) ^{2}}

Solution steps

L {3 e^{- 2 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)}

= 3 L {t e^{- 2 t}}

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

= 3 \cdot \frac{1}{( s + 2 ) ^{2}}

Refine

3 \frac{1}{( s + 2 ) ^{2}} : \frac{3}{( s + 2 ) ^{2}}

= \frac{3}{( s + 2 ) ^{2}}

\frac{d}{d x} (3 (x - 1)^{2})

\int \frac{1}{sin ^{4} ( x )} d x

\frac{d}{d x} (z (x) + x^{2})

\int_{0}^{1} t 1 + t^{2} + t^{4} d t

x \to 3 - lim (sin (π x) + 1)

What is laplacetransform 3te^{-2t} ?
The answer to laplacetransform 3te^{-2t} is 3/((s+2)^2)