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

Lösung

inverse laplace transformation

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

- sin (t) + t

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

= L^{- 1} {- \frac{1}{s ^{2} + 1} + \frac{1}{s ^{2}}}

Wende die lineare Eigenschaftder inversen Laplace-Transformation an:

Für Funktionen

f (s), g (s)

und Konstanten

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= - L^{- 1} {\frac{1}{s ^{2} + 1}} + L^{- 1} {\frac{1}{s ^{2}}}

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

L^{- 1} {\frac{1}{s ^{2}}} : t

= - sin (t) + t

x \to 0 + lim (arccot (x))

\int (2 x^{2} + 3 x - 3) (5 x + 3) d x

d er i v a t i v e f (x) = \frac{x ^{4}}{8} - 8 x

x \to \infty lim (5 + \frac{1}{x})

x \to 3 lim (4 + 4 (- 4))