What is laplacetransform e^{3t}(9-4t+10sin(t/2)) ?

The answer to laplacetransform e^{3t}(9-4t+10sin(t/2)) is 9/(s-3)-4/((s-3)^2)+(20)/(4(s-3)^2+1)

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laplacetransform e^{3t}(9-4t+10sin(t/2))

laplace transform

e^{3 t} (9 - 4 t + 10 sin (\frac{t}{2}))

\frac{9}{s - 3} - \frac{4}{( s - 3 ) ^{2}} + \frac{20}{4 ( s - 3 ) ^{2} + 1}

Solution steps

L {e^{3 t} (- 4 t + 10 sin (\frac{t}{2}) + 9)}

Apply transform rule:

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

then

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

For

e^{3 t} (9 - 4 t + 10 sin (\frac{t}{2})) : f (t) = (9 - 4 t + 10 sin (\frac{t}{2})), a = 3

= L {(9 - 4 t + 10 sin (\frac{t}{2}))} (s - 3)

L {(9 - 4 t + 10 sin (\frac{t}{2}))} : \frac{9}{s} - \frac{4}{s ^{2}} + \frac{20}{4 s ^{2} + 1}

= \frac{9}{( s - 3 )} - \frac{4}{( s - 3 ) ^{2}} + \frac{20}{4 ( s - 3 ) ^{2} + 1}

= \frac{9}{s - 3} - \frac{4}{( s - 3 ) ^{2}} + \frac{20}{4 ( s - 3 ) ^{2} + 1}

x \to 0 + lim (x ln (e^{x} - 1))

f (x) = \frac{x ^{2} - 99}{x - 10}

f (x) = e^{5 x^{2}}

\frac{d y}{d x} = 2 y + x^{2} + 7

\int 16 x^{3} ln (x) d x

What is laplacetransform e^{3t}(9-4t+10sin(t/2)) ?
The answer to laplacetransform e^{3t}(9-4t+10sin(t/2)) is 9/(s-3)-4/((s-3)^2)+(20)/(4(s-3)^2+1)