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Beliebt Rechnen >

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

Lösung

inverse laplace transformation

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

Lösung

e^{- t} cos (t)

Schritte zur Lösung

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

Wende inverse Transformationsregel an: if

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

dann

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

Für

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

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

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

= e^{- t} cos (t)

Beliebte Beispiele

integral of (11x)^2

\int (11 x)^{2} d x

integral of 1/((x+4)^{7/2)}

\int \frac{1}{( x + 4 ) ^{\frac{7}{2}}} d x

y^{^{'}} + 2 x y = 1

(\partial)/(\partial x)(e^t)

\frac{\partial}{\partial x} (e^{t})

limit as x approaches 1 of x^3-2x+2

x \to 1 lim (x^{3} - 2 x + 2)