What is laplacetransform 2t*cos(t) ?

The answer to laplacetransform 2t*cos(t) is -(2(-s^2+1))/((s^2+1)^2)

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laplacetransform 2t*cos(t)

laplace transform

2 t \cdot cos (t)

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

Solution steps

L {2 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)}

= 2 L {t cos (t)}

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

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

Refine

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

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

\int 3 t cos (2 t) d t

x \to 8 lim (\frac{∣ 8 - x ∣}{8 - x})

\int \frac{x ^{2} + 1}{x ^{2} + 2} d x

x \to 3 - lim (\frac{7 - x}{x - 3})

\int \frac{x}{x ^{4} - 1} d x

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