What is laplacetransform e^{-5t}*e^{25t}cos(20t) ?

The answer to laplacetransform e^{-5t}*e^{25t}cos(20t) is (s-20)/((s-20)^2+400)

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laplacetransform e^{-5t}*e^{25t}cos(20t)

laplace transform

e^{- 5 t} \cdot e^{25 t} cos (20 t)

\frac{s - 20}{( s - 20 ) ^{2} + 400}

Solution steps

L {e^{- 5 t} e^{25 t} cos (20 t)}

Expand

e^{- 5 t} e^{25 t} cos (20 t) : e^{20 t} cos (20 t)

= L {e^{20 t} cos (20 t)}

Apply transform rule:

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

then

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

For

e^{20 t} cos (20 t) : f (t) = cos (20 t), a = 20

= L {cos (20 t)} (s - 20)

L {cos (20 t)} : \frac{s}{s ^{2} + 400}

= \frac{( s - 20 )}{( s - 20 ) ^{2} + 400}

= \frac{s - 20}{( s - 20 ) ^{2} + 400}

\int (1 - t^{2})^{3} d t

y = x^{- 3} + 5 x^{- 2}

y^{^{'}} = \frac{x - y}{x + y}, y (0) = 1

\frac{d}{d x} (\frac{sin ( x ) - x}{x ^{2}})

\frac{d}{d x} (e^{x^{4} + x})

What is laplacetransform e^{-5t}*e^{25t}cos(20t) ?
The answer to laplacetransform e^{-5t}*e^{25t}cos(20t) is (s-20)/((s-20)^2+400)