What is laplacetransform e^{3t}cos(6t) ?

The answer to laplacetransform e^{3t}cos(6t) is (s-3)/((s-3)^2+36)

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laplacetransform e^{3t}cos(6t)

laplace transform

e^{3 t} cos (6 t)

\frac{s - 3}{( s - 3 ) ^{2} + 36}

Solution steps

L {e^{3 t} cos (6 t)}

Apply transform rule:

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

then

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

For

e^{3 t} cos (6 t) : f (t) = cos (6 t), a = 3

= L {cos (6 t)} (s - 3)

L {cos (6 t)} : \frac{s}{s ^{2} + 36}

= \frac{( s - 3 )}{( s - 3 ) ^{2} + 36}

= \frac{s - 3}{( s - 3 ) ^{2} + 36}

\int 3 a^{7} x^{6} d x

\int (x + 1) e^{- x} d x

\int x e^{0.2 x} d x

d er i v a t i v e f (x) = x^{3} + 3 x

d er i v a t i v e f (x) = \frac{x + 9}{x - 9}

What is laplacetransform e^{3t}cos(6t) ?
The answer to laplacetransform e^{3t}cos(6t) is (s-3)/((s-3)^2+36)