laplacetransform e^{5t}t

Lösung

laplace transformation

e^{5 t} t

\frac{1}{( s - 5 ) ^{2}}

Schritte zur Lösung

L {e^{5 t} t}

Wende Laplace-Transformationstabelle an:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

Für

e^{5 t} t : f (t) = e^{5 t}, k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{5 t}})

L {e^{5 t}} : \frac{1}{s - 5}

\frac{d}{d s} (\frac{1}{s - 5}) = - \frac{1}{( s - 5 ) ^{2}}

= (- 1)^{1} (- \frac{1}{( s - 5 ) ^{2}})

= \frac{1}{( s - 5 ) ^{2}}

\frac{d}{d x} (x^{2} - 6 x + 9)

\int_{1}^{2} \frac{1}{x ( ln ( x ) ) ^{1}} d x

\int_{1}^{\infty} \frac{1}{1 + e ^{x}} d x

a re a 2 x, 5, \frac{2}{x ^{2}}

x \to \infty lim (2 x - 4 x^{2} - 2 x)