What is laplacetransform 3tcos(t) ?

The answer to laplacetransform 3tcos(t) is -(3(-s^2+1))/((s^2+1)^2)

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laplacetransform 3tcos(t)

laplace transform

3 t cos (t)

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

Solution steps

L {3 t cos (t)}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= 3 L {t cos (t)}

L {t cos (t)} : - \frac{- s ^{2} + 1}{( s ^{2} + 1 ) ^{2}}

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

Refine

3 (- \frac{- s ^{2} + 1}{( s ^{2} + 1 ) ^{2}}) : - \frac{3 ( - s ^{2} + 1 )}{( s ^{2} + 1 ) ^{2}}

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

\frac{d x}{d t} = x + t

\frac{d}{d x} (\frac{1}{3} x^{3} + \frac{1}{2} x^{2})

f (x) = 2 sec (x), at x = \frac{π}{6}

(\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 7 y^{3})

\frac{\partial}{\partial x} (\frac{x ^{α} y ^{β}}{y ^{1 - α} x ^{1 - β}})

What is laplacetransform 3tcos(t) ?
The answer to laplacetransform 3tcos(t) is -(3(-s^2+1))/((s^2+1)^2)