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Beliebt Rechnen >

inverselaplace 3/((s+1)^2+9)

Lösung

inverse laplace transformation

\frac{3}{( s + 1 ) ^{2} + 9}

Lösung

e^{- t} sin (3 t)

Schritte zur Lösung

L^{- 1} {\frac{3}{( s + 1 ) ^{2} + 9}}

Wende inverse Transformationsregel an: if

L^{- 1} {F (s)} = f (t)

dann

L^{- 1} {F (s - a)} = e^{a t} f (t)

Für

\frac{3}{( s + 1 ) ^{2} + 9} : a = - 1, F (s) = \frac{3}{s ^{2} + 9}

= e^{- t} L^{- 1} {\frac{3}{s ^{2} + 9}}

L^{- 1} {\frac{3}{s ^{2} + 9}} : sin (3 t)

= e^{- t} sin (3 t)

Beliebte Beispiele

derivative of tan(13x)

\frac{d}{d x} (tan (13 x))

derivative 2e^{4x}cos(5x)

d er i v a t i v e 2 e^{4 x} cos (5 x)

(\partial)/(\partial x)(ln(x^7-y^3))

\frac{\partial}{\partial x} (ln (x^{7} - y^{3}))

derivative of-5/(\sqrt[3]{x})

\frac{d}{d x} (- \frac{5}{3 x})

extreme f(x)=e^{a/x}

e x t re m e f (x) = e^{\frac{a}{x}}