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Beliebt Rechnen >

laplacetransform (1+e^t)^2

Lösung

laplace transformation

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

Lösung

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

Schritte zur Lösung

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

Schreibe

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

um:

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

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

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

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

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

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

Fasse

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

zusammen:

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

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

Beliebte Beispiele

(\partial)/(\partial x)(8+xln(xy-5))

\frac{\partial}{\partial x} (8 + x ln (x y - 5))

integral of (x^2)/u

\int \frac{x ^{2}}{u} d u

derivative f(x)=x^2arctan(4x)

d er i v a t i v e f (x) = x^{2} arctan (4 x)

(\partial)/(\partial y)(e^x+y^2)

\frac{\partial}{\partial y} (e^{x} + y^{2})

derivative h(x)= 7/(x^2)

d er i v a t i v e h (x) = \frac{7}{x ^{2}}