What is laplacetransform e^{-43t}*e^{72t}cos(77t) ?

The answer to laplacetransform e^{-43t}*e^{72t}cos(77t) is (s-29)/((s-29)^2+5929)

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laplacetransform e^{-43t}*e^{72t}cos(77t)

laplace transform

e^{- 43 t} \cdot e^{72 t} cos (77 t)

\frac{s - 29}{( s - 29 ) ^{2} + 5929}

Solution steps

L {e^{- 43 t} e^{72 t} cos (77 t)}

Expand

e^{- 43 t} e^{72 t} cos (77 t) : e^{29 t} cos (77 t)

= L {e^{29 t} cos (77 t)}

Apply transform rule:

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

then

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

For

e^{29 t} cos (77 t) : f (t) = cos (77 t), a = 29

= L {cos (77 t)} (s - 29)

L {cos (77 t)} : \frac{s}{s ^{2} + 5929}

= \frac{( s - 29 )}{( s - 29 ) ^{2} + 5929}

= \frac{s - 29}{( s - 29 ) ^{2} + 5929}

\int 5 sin (\frac{x}{4}) d x

\frac{d}{d s} (\frac{1}{s ^{2}})

4 x^{- \frac{1}{8}}

(\frac{3 x ^{2}}{( 2 x + 4 )})^{3}

\frac{d y}{d x} = \frac{( 2 y + 5 ) ^{2}}{( 8 x + 9 ) ^{2}}

What is laplacetransform e^{-43t}*e^{72t}cos(77t) ?
The answer to laplacetransform e^{-43t}*e^{72t}cos(77t) is (s-29)/((s-29)^2+5929)