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Beliebt Rechnen >

laplacetransform x^2e^{2x}

Lösung

laplace transformation

x^{2} e^{2 x}

Lösung

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

Schritte zur Lösung

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

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

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

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

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

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

Beliebte Beispiele

derivative of 2sec^2(2x)

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

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

\int_{0}^{π} sin (x^{2}) d x

integral of cot^3(x)

\int cot^{3} (x) d x

tangent f(x)=sqrt(x+8),(8,4)

t an g e n t f (x) = x + 8, (8, 4)

integral of (2x)/(9-4x^2)

\int \frac{2 x}{9 - 4 x ^{2}} d x