What is laplacetransform f(t)=3sin(4t)-2e^{2t} ?

The answer to laplacetransform f(t)=3sin(4t)-2e^{2t} is (12)/(s^2+16)-2/(s-2)

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laplacetransform f(t)=3sin(4t)-2e^{2t}

laplace transform

f (t) = 3 sin (4 t) - 2 e^{2 t}

\frac{12}{s ^{2} + 16} - \frac{2}{s - 2}

Solution steps

L {3 sin (4 t) - 2 e^{2 t}}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= 3 L {sin (4 t)} - 2 L {e^{2 t}}

L {sin (4 t)} : \frac{4}{s ^{2} + 16}

L {e^{2 t}} : \frac{1}{s - 2}

= 3 \cdot \frac{4}{s ^{2} + 16} - 2 \cdot \frac{1}{s - 2}

Refine

3 \frac{4}{s ^{2} + 16} - 2 \frac{1}{s - 2} : \frac{12}{s ^{2} + 16} - \frac{2}{s - 2}

= \frac{12}{s ^{2} + 16} - \frac{2}{s - 2}

h (t) = 6 ln (t^{8})

\frac{d}{d x} (144 - x)

\int (5 - x^{3})^{4} x^{2} d x

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

x^{2} + 4, - x^{2} - 1, [- 2, 3]

What is laplacetransform f(t)=3sin(4t)-2e^{2t} ?
The answer to laplacetransform f(t)=3sin(4t)-2e^{2t} is (12)/(s^2+16)-2/(s-2)