What is laplacetransform sin(2t)*e^{3t} ?

The answer to laplacetransform sin(2t)*e^{3t} is 2/((s-3)^2+4)

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laplacetransform sin(2t)*e^{3t}

laplace transform

sin (2 t) \cdot e^{3 t}

\frac{2}{( s - 3 ) ^{2} + 4}

Solution steps

L {e^{3 t} sin (2 t)}

Apply transform rule:

L {f (t)} = F (s)

then

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

For

sin (2 t) e^{3 t} : f (t) = sin (2 t), a = 3

= L {sin (2 t)} (s - 3)

L {sin (2 t)} : \frac{2}{s ^{2} + 4}

= \frac{2}{( s - 3 ) ^{2} + 4}

\frac{d}{d x} (arcsin (5 x^{4}))

\int ln (2 + x) d x

(- 1, 1), (1, - 2)

x \to 0 lim (\frac{tan ( 2 ) ( x )}{x})

2 x^{8} e^{x}

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