laplacetransform t^2(8e^{2t}-6sin(2t))

Lösung

laplace transformation

t^{2} (8 e^{2 t} - 6 sin (2 t))

- \frac{8 ( - 2 s ^{6} + 9 s ^{5} - 78 s ^{4} + 96 s ^{3} - 96 s ^{2} - 144 s - 32 )}{( s - 2 ) ^{3} ( s ^{2} + 4 ) ^{3}}

Schritte zur Lösung

L {t^{2} (8 e^{2 t} - 6 sin (2 t))}

Wende Laplace-Transformationstabelle an:

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

Für

t^{2} (8 e^{2 t} - 6 sin (2 t)) : f (t) = (8 e^{2 t} - 6 sin (2 t)), k = 2

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {(8 e^{2 t} - 6 sin (2 t))})

L {(8 e^{2 t} - 6 sin (2 t))} : \frac{8}{s - 2} - \frac{12}{s ^{2} + 4}

\frac{d ^{2}}{d s ^{2}} (\frac{8}{s - 2} - \frac{12}{s ^{2} + 4}) = - \frac{8 ( - 2 s ^{6} + 9 s ^{5} - 78 s ^{4} + 96 s ^{3} - 96 s ^{2} - 144 s - 32 )}{( s - 2 ) ^{3} ( s ^{2} + 4 ) ^{3}}

= (- 1)^{2} (- \frac{8 ( - 2 s ^{6} + 9 s ^{5} - 78 s ^{4} + 96 s ^{3} - 96 s ^{2} - 144 s - 32 )}{( s - 2 ) ^{3} ( s ^{2} + 4 ) ^{3}})

= - \frac{8 ( - 2 s ^{6} + 9 s ^{5} - 78 s ^{4} + 96 s ^{3} - 96 s ^{2} - 144 s - 32 )}{( s - 2 ) ^{3} ( s ^{2} + 4 ) ^{3}}

\frac{d}{d x} (x^{2} - 39.5 x + 120 + \frac{125}{x})

x \to 0 - lim (\frac{1}{x ^{3} - x})

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