What is laplacetransform sin(3t)e^{4t} ?

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

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laplacetransform sin(3t)e^{4t}

laplace transform

sin (3 t) e^{4 t}

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

Solution steps

L {e^{4 t} sin (3 t)}

Apply transform rule:

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

then

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

For

sin (3 t) e^{4 t} : f (t) = sin (3 t), a = 4

= L {sin (3 t)} (s - 4)

L {sin (3 t)} : \frac{3}{s ^{2} + 9}

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

\int sin (\frac{1}{2}) x d x

e^{6}, e^{x}, x = 0

x \to + 2 - lim (\frac{∣ x - x ∣}{x - 2})

\frac{d y}{d x} = \frac{3 x}{3 + x ^{2}}

y^{^{'}} + x \cdot e^{- x^{\frac{2}{2}}} = 0

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