What is laplacetransform e^{2t}cos(3t) ?

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

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laplacetransform e^{2t}cos(3t)

laplace transform

e^{2 t} cos (3 t)

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

Solution steps

L {e^{2 t} cos (3 t)}

Apply transform rule:

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

then

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

For

e^{2 t} cos (3 t) : f (t) = cos (3 t), a = 2

= L {cos (3 t)} (s - 2)

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

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

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

\int + \frac{x ^{4} + 12 x ^{2} + 1}{x ^{5} + 20 x ^{3} + 5 x} d x

\int 2 e^{x} - 8 x d x

y = \frac{5}{1 + x ^{2}}, (4, 0.29412)

f (x) = 6 x^{2} cot (x)

x \to \infty lim (2 x - 2 x)

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