What is laplacetransform e^{-5t}sin(7t) ?

The answer to laplacetransform e^{-5t}sin(7t) is 7/((s+5)^2+49)

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laplacetransform e^{-5t}sin(7t)

laplace transform

e^{- 5 t} sin (7 t)

\frac{7}{( s + 5 ) ^{2} + 49}

Solution steps

L {e^{- 5 t} sin (7 t)}

Apply transform rule:

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

then

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

For

e^{- 5 t} sin (7 t) : f (t) = sin (7 t), a = - 5

= L {sin (7 t)} (s + 5)

L {sin (7 t)} : \frac{7}{s ^{2} + 49}

= \frac{7}{( s + 5 ) ^{2} + 49}

\frac{d}{d x} (arctan (2 x^{3}))

\int \frac{( 5 x + 7 )}{x ^{2} + 4 x + 4} d x

\frac{d}{d x} (10000 - 9000 e^{- 0.3 x})

\frac{d}{d x} (\frac{x ^{2}}{e ^{3 - 4 x}})

What is laplacetransform e^{-5t}sin(7t) ?
The answer to laplacetransform e^{-5t}sin(7t) is 7/((s+5)^2+49)