What is laplacetransform 12te^{10t} ?

The answer to laplacetransform 12te^{10t} is (12)/((s-10)^2)

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laplacetransform 12te^{10t}

laplace transform

12 t e^{10 t}

\frac{12}{( s - 10 ) ^{2}}

Solution steps

L {12 e^{10 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)}

= 12 L {t e^{10 t}}

L {t e^{10 t}} : \frac{1}{( s - 10 ) ^{2}}

= 12 \cdot \frac{1}{( s - 10 ) ^{2}}

Refine

12 \frac{1}{( s - 10 ) ^{2}} : \frac{12}{( s - 10 ) ^{2}}

= \frac{12}{( s - 10 ) ^{2}}

What is laplacetransform 12te^{10t} ?
The answer to laplacetransform 12te^{10t} is (12)/((s-10)^2)