What is laplacetransform e^{3t}sin(6t) ?

The answer to laplacetransform e^{3t}sin(6t) is 6/((s-3)^2+36)

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laplacetransform e^{3t}sin(6t)

laplace transform

e^{3 t} sin (6 t)

\frac{6}{( s - 3 ) ^{2} + 36}

Solution steps

L {e^{3 t} sin (6 t)}

Apply transform rule:

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

then

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

For

e^{3 t} sin (6 t) : f (t) = sin (6 t), a = 3

= L {sin (6 t)} (s - 3)

L {sin (6 t)} : \frac{6}{s ^{2} + 36}

= \frac{6}{( s - 3 ) ^{2} + 36}

y = x

\frac{\partial}{\partial w} (x e^{w})

\frac{lo g _{2} ( x )}{x}

\int_{0}^{6} x 36 - x^{2} d x

\int - x^{4} ln (x) d x

What is laplacetransform e^{3t}sin(6t) ?
The answer to laplacetransform e^{3t}sin(6t) is 6/((s-3)^2+36)