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Beliebt Rechnen >

laplacetransform f(t)=(1+e^{4t})^2

Lösung

laplace transformation

f (t) = (1 + e^{4 t})^{2}

Lösung

\frac{1}{s} + \frac{2}{s - 4} + \frac{1}{s - 8}

Schritte zur Lösung

L {(1 + e^{4 t})^{2}}

Schreibe

(1 + e^{4 t})^{2}

um:

1 + 2 e^{4 t} + e^{8 t}

= L {1 + 2 e^{4 t} + e^{8 t}}

Verwende die lineare Eigenschaft der Laplace-Transformation:

Für Funktionen

f (t), g (t)

und Konstanten

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {1} + 2 L {e^{4 t}} + L {e^{8 t}}

L {1} : \frac{1}{s}

L {e^{4 t}} : \frac{1}{s - 4}

L {e^{8 t}} : \frac{1}{s - 8}

= \frac{1}{s} + 2 \cdot \frac{1}{s - 4} + \frac{1}{s - 8}

Fasse

\frac{1}{s} + 2 \frac{1}{s - 4} + \frac{1}{s - 8}

zusammen:

\frac{1}{s} + \frac{2}{s - 4} + \frac{1}{s - 8}

= \frac{1}{s} + \frac{2}{s - 4} + \frac{1}{s - 8}

Beliebte Beispiele

integral of (3x+1)/(x(x+1)^2)

\int \frac{3 x + 1}{x ( x + 1 ) ^{2}} d x

laplacetransform e^{-2t-5}

l a pl a ce t r an s f or m e^{- 2 t - 5}

(\partial)/(\partial x)(y*ln(x))

\frac{\partial}{\partial x} (y \cdot ln (x))

integral of (x+1)/(x^3-x^2)

\int \frac{x + 1}{x ^{3} - x ^{2}} d x

integral from 0 to pi of sin^2(x)

\int_{0}^{π} sin^{2} (x) d x