inverselaplace (-2)/((s^2+1)^2)

Lösung

inverse laplace transformation

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

- (sin (t) - t cos (t))

Schritte zur Lösung

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

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

Wende die konstante Multiplikationseigenschaft der inversen Laplace-Transformation an:

Für Funktionen

f (t)

und Konstante

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

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

Verwende inverse Laplace-Transformationstabelle:

L^{- 1} {\frac{2 a ^{3}}{( s ^{2} + a ^{2} ) ^{2}}} = sin (a t) - a t cos (a t)

L^{- 1} {\frac{2 \cdot 1 ^{3}}{( s ^{2} + 1 ^{2} ) ^{2}}} = sin (t) - t cos (t)

= - 1 \cdot (sin (t) - t cos (t))

= - (sin (t) - t cos (t))

\int_{0}^{π} sin^{4} (3 t) d t

\int 40 x^{3} + 20 d x

\int 20 - (20)^{2} - x^{2} d x

\int (4 x^{3} + 3^{x}) d x

\int \frac{( e ^{x} - 2 ) e ^{x}}{e ^{x} + 1} d x