What is laplacetransform 9t^2e^{2t} ?

The answer to laplacetransform 9t^2e^{2t} is (18)/((s-2)^3)

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laplacetransform 9t^2e^{2t}

laplace transform

9 t^{2} e^{2 t}

\frac{18}{( s - 2 ) ^{3}}

Solution steps

L {9 e^{2 t} t^{2}}

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)}

= 9 L {t^{2} e^{2 t}}

L {t^{2} e^{2 t}} : \frac{2}{( s - 2 ) ^{3}}

= 9 \cdot \frac{2}{( s - 2 ) ^{3}}

Refine

9 \frac{2}{( s - 2 ) ^{3}} : \frac{18}{( s - 2 ) ^{3}}

= \frac{18}{( s - 2 ) ^{3}}

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

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

\int 8 x^{2} ln (x) d x

\frac{\partial}{\partial x} (2 x^{2} y + 9 x y^{3})

\frac{d}{d t} (sin (t) + cos (t))

What is laplacetransform 9t^2e^{2t} ?
The answer to laplacetransform 9t^2e^{2t} is (18)/((s-2)^3)