What is laplacetransform 2tcos(2t) ?

The answer to laplacetransform 2tcos(2t) is -(2(-s^2+4))/((s^2+4)^2)

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laplacetransform 2tcos(2t)

laplace transform

2 t cos (2 t)

- \frac{2 ( - s ^{2} + 4 )}{( s ^{2} + 4 ) ^{2}}

Solution steps

L {2 t cos (2 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 (2 t)}

L {t cos (2 t)} : - \frac{- s ^{2} + 4}{( s ^{2} + 4 ) ^{2}}

= 2 (- \frac{- s ^{2} + 4}{( s ^{2} + 4 ) ^{2}})

Refine

2 (- \frac{- s ^{2} + 4}{( s ^{2} + 4 ) ^{2}}) : - \frac{2 ( - s ^{2} + 4 )}{( s ^{2} + 4 ) ^{2}}

= - \frac{2 ( - s ^{2} + 4 )}{( s ^{2} + 4 ) ^{2}}

\frac{d}{d x} (7 x + 6)

\frac{d}{d x} (\frac{1 + csc ( x ^{2} )}{1 - cot ( x ^{2} )})

\int \frac{k}{x + 1} d x

\int_{0}^{5} 12 \frac{t}{t + 1} d t

\int csc (9 x) d x

What is laplacetransform 2tcos(2t) ?
The answer to laplacetransform 2tcos(2t) is -(2(-s^2+4))/((s^2+4)^2)