What is inverse oflaplace 3/((s-2)^2) ?

The answer to inverse oflaplace 3/((s-2)^2) is e^{2t}*3t

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inverse oflaplace 3/((s-2)^2)

inverse laplace

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

e^{2 t} \cdot 3 t

Solution steps

L^{- 1} {\frac{3}{( s - 2 ) ^{2}}}

Apply inverse transform rule:

L^{- 1} {F (s)} = f (t)

then

L^{- 1} {F (s - a)} = e^{a t} f (t)

For

\frac{3}{( s - 2 ) ^{2}} : a = 2, F (s) = \frac{3}{s ^{2}}

= e^{2 t} L^{- 1} {\frac{3}{s ^{2}}}

L^{- 1} {\frac{3}{s ^{2}}} : 3 t

= e^{2 t} \cdot 3 t

\frac{\partial}{\partial x} (arctan (7 x t))

\int - 2 sin (2 x) d x

\int \frac{sin ( θ )}{θ} d θ

\int \frac{3 e ^{2 x}}{e ^{2 x} + 13 e ^{x} + 40} d x

x \to 0 lim (- x^{2} + 3 x + a)

What is inverse oflaplace 3/((s-2)^2) ?
The answer to inverse oflaplace 3/((s-2)^2) is e^{2t}*3t