What is laplacetransform e^{2t}cos(3t+5) ?

The answer to laplacetransform e^{2t}cos(3t+5) is (cos(5)(s-2)-3sin(5))/((s-2)^2+9)

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laplacetransform e^{2t}cos(3t+5)

laplace transform

e^{2 t} cos (3 t + 5)

\frac{cos ( 5 ) ( s - 2 ) - 3 sin ( 5 )}{( s - 2 ) ^{2} + 9}

Solution steps

L {e^{2 t} cos (3 t + 5)}

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 + 5) : f (t) = cos (3 t + 5), a = 2

= L {cos (3 t + 5)} (s - 2)

L {cos (3 t + 5)} : \frac{cos ( 5 ) s - 3 sin ( 5 )}{s ^{2} + 9}

= \frac{cos ( 5 ) ( s - 2 ) - 3 sin ( 5 )}{( s - 2 ) ^{2} + 9}

\frac{1}{4 + x}

z \to 0 lim (\frac{8}{z ^{3}} + \frac{5}{z} + 2)

\frac{d}{d x} (x^{5} - 2 x^{3} + x)

\int (x + 3) 6 x + x^{2} d x

\frac{d}{d t} (1 - t)

What is laplacetransform e^{2t}cos(3t+5) ?
The answer to laplacetransform e^{2t}cos(3t+5) is (cos(5)(s-2)-3sin(5))/((s-2)^2+9)