What is laplacetransform 9/4 t^2e^{5t} ?

The answer to laplacetransform 9/4 t^2e^{5t} is 9/(2(s-5)^3)

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laplacetransform 9/4 t^2e^{5t}

laplace transform

\frac{9}{4} t^{2} e^{5 t}

\frac{9}{2 ( s - 5 ) ^{3}}

Solution steps

L {\frac{9}{4} e^{5 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)}

= \frac{9}{4} L {t^{2} e^{5 t}}

L {t^{2} e^{5 t}} : \frac{2}{( s - 5 ) ^{3}}

= \frac{9}{4} \cdot \frac{2}{( s - 5 ) ^{3}}

Refine

\frac{9}{4} \frac{2}{( s - 5 ) ^{3}} : \frac{9}{2 ( s - 5 ) ^{3}}

= \frac{9}{2 ( s - 5 ) ^{3}}

\int \frac{4 x - 1}{x ^{2} + x - 2} d x

x \to c lim ((8)^{\frac{2}{3}})

x \to 1 - lim (7 ∣ x + 1 ∣ - 4)

\int \frac{4}{3} x^{2} d x

arcsin (x - 2)

What is laplacetransform 9/4 t^2e^{5t} ?
The answer to laplacetransform 9/4 t^2e^{5t} is 9/(2(s-5)^3)