laplacetransform (t+1)^2

Lösung

laplace transformation

(t + 1)^{2}

\frac{2}{s ^{3}} + \frac{2}{s ^{2}} + \frac{1}{s}

Schritte zur Lösung

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

Schreibe

(t + 1)^{2}

um:

t^{2} + 2 t + 1

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

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

L {t^{2}} : \frac{2}{s ^{3}}

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

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

= \frac{2}{s ^{3}} + 2 \cdot \frac{1}{s ^{2}} + \frac{1}{s}

Fasse

\frac{2}{s ^{3}} + 2 \frac{1}{s ^{2}} + \frac{1}{s}

zusammen:

\frac{2}{s ^{3}} + \frac{2}{s ^{2}} + \frac{1}{s}

= \frac{2}{s ^{3}} + \frac{2}{s ^{2}} + \frac{1}{s}

\int \frac{4 x + 6}{( x ^{2} + 2 ) \cdot ( x + 2 )} d x

d er i v a t i v e f (x) = x^{\frac{5}{3}} - x^{\frac{2}{3}}

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

ma c l a u r in \frac{1}{x - 3}

\int \frac{2 e ^{2 r}}{7 + e ^{2 r}} d r