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Beliebt Rechnen >

laplacetransform e^{-2t}(t^2+4t+5)

Lösung

laplace transformation

e^{- 2 t} (t^{2} + 4 t + 5)

Lösung

\frac{5 s ^{2} + 24 s + 30}{( s + 2 ) ^{3}}

Schritte zur Lösung

L {e^{- 2 t} (t^{2} + 4 t + 5)}

Wende Transformationsregel an: wenn

L {f (t)} = F (s)

dann

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

Für

e^{- 2 t} (t^{2} + 4 t + 5) : f (t) = (t^{2} + 4 t + 5), a = - 2

= L {(t^{2} + 4 t + 5)} (s + 2)

L {(t^{2} + 4 t + 5)} : \frac{2}{s ^{3}} + \frac{4}{s ^{2}} + \frac{5}{s}

= \frac{2}{( s + 2 ) ^{3}} + \frac{4}{( s + 2 ) ^{2}} + \frac{5}{( s + 2 )}

= \frac{2}{( s + 2 ) ^{3}} + \frac{4}{( s + 2 ) ^{2}} + \frac{5}{s + 2}

Vereinfache

\frac{2}{( s + 2 ) ^{3}} + \frac{4}{( s + 2 ) ^{2}} + \frac{5}{s + 2} : \frac{5 s ^{2} + 24 s + 30}{( s + 2 ) ^{3}}

= \frac{5 s ^{2} + 24 s + 30}{( s + 2 ) ^{3}}

Beliebte Beispiele

integral from a to 2a of (a-(a^3)/(x^2))

\int_{a}^{2 a} (a - \frac{a ^{3}}{x ^{2}}) d x

derivative of 2/(sqrt(x^2+5))

\frac{d}{d x} (\frac{2}{x ^{2} + 5})

integral of cos(x)cos(sin(x))

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

limit as x approaches+5-of 5/((x-5)^3)

x \to + 5 - lim (\frac{5}{( x - 5 ) ^{3}})

integral of ((3x+5)^3)/(10)

\int \frac{( 3 x + 5 ) ^{3}}{10} d x