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

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

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

laplace transform

e^{3 x} sin (6 x)

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

Solution steps

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

Apply transform rule:

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

then

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

For

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

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

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

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

\int \frac{x}{x - 21} d x

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

\int_{0}^{1} x^{2} + 1 d x

\frac{1}{s ( ( s - 1 ) ^{2} + 1 )}

\frac{d}{d y} (\frac{y ^{2}}{4})

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