What is laplacetransform g(t)=3+t^5+sin(pit) ?

The answer to laplacetransform g(t)=3+t^5+sin(pit) is 3/s+(120)/(s^6)+pi/(s^2+pi^2)

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laplacetransform g(t)=3+t^5+sin(pit)

laplace transform

g (t) = 3 + t^{5} + sin (π t)

\frac{3}{s} + \frac{120}{s ^{6}} + \frac{π}{s ^{2} + π ^{2}}

Solution steps

L {3 + t^{5} + sin (π 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)}

= L {3} + L {t^{5}} + L {sin (π t)}

L {3} : \frac{3}{s}

L {t^{5}} : \frac{120}{s ^{6}}

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

= \frac{3}{s} + \frac{120}{s ^{6}} + \frac{π}{s ^{2} + π ^{2}}

x^{3} (x - 6)^{2}

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

\frac{\partial}{\partial x} (\frac{2 x - y}{x + 4 y})

\int e^{c o s (t)} d t

What is laplacetransform g(t)=3+t^5+sin(pit) ?
The answer to laplacetransform g(t)=3+t^5+sin(pit) is 3/s+(120)/(s^6)+pi/(s^2+pi^2)