laplacetransform t*cos(t)

Lösung

laplace transformation

t \cdot cos (t)

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

Schritte zur Lösung

L {t cos (t)}

Wende Laplace-Transformationstabelle an:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

Für

t cos (t) : f (t) = cos (t), k = 1

= (- 1)^{1} \frac{d}{d s} (L {cos (t)})

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

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

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

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

\frac{d}{d x} (sinh^{3} (\frac{1}{x}))

\int (sin (x) - 6 cos (x)) d x

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