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Beliebt Rechnen >

laplacetransform x^2e^{3x}

Lösung

laplace transformation

x^{2} e^{3 x}

Lösung

\frac{2}{( s - 3 ) ^{3}}

Schritte zur Lösung

L {e^{3 x} x^{2}}

Wende Laplace-Transformationstabelle an:

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

Für

x^{2} e^{3 x} : f (x) = e^{3 x}, k = 2

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {e^{3 x}})

L {e^{3 x}} : \frac{1}{s - 3}

\frac{d ^{2}}{d s ^{2}} (\frac{1}{s - 3}) = \frac{2}{( s - 3 ) ^{3}}

= (- 1)^{2} \frac{2}{( s - 3 ) ^{3}}

= \frac{2}{( s - 3 ) ^{3}}

Beliebte Beispiele

derivative of (arctan(2x)^2)

\frac{d}{d x} ((arctan (2 x))^{2})

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

derivative of x^2sqrt(x)-5x

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

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