What is laplacetransform e^{2t}cos(t) ?

The answer to laplacetransform e^{2t}cos(t) is (s-2)/((s-2)^2+1)

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laplacetransform e^{2t}cos(t)

laplace transform

e^{2 t} cos (t)

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

Solution steps

L {e^{2 t} cos (t)}

Apply transform rule:

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

then

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

For

e^{2 t} cos (t) : f (t) = cos (t), a = 2

= L {cos (t)} (s - 2)

L {cos (t)} : \frac{s}{s ^{2} + 1}

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

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

l a pl a ce t r an s f or m - 2 sin (3 t)

x \to \frac{π}{2} lim (\frac{cos ( x )}{cot ( x )})

\frac{\partial}{\partial x} (x y sin (x y))

\int \frac{e ^{x}}{4 + e ^{x}} d x

\frac{d}{d t} (t^{2} + 1)

What is laplacetransform e^{2t}cos(t) ?
The answer to laplacetransform e^{2t}cos(t) is (s-2)/((s-2)^2+1)