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Beliebt Rechnen >

laplacetransform e^{3t}(t^2+4)

Lösung

laplace transformation

e^{3 t} (t^{2} + 4)

Lösung

\frac{2}{( s - 3 ) ^{3}} + \frac{4}{s - 3}

Schritte zur Lösung

L {e^{3 t} (t^{2} + 4)}

Wende Transformationsregel an: wenn

L {f (t)} = F (s)

dann

L {e^{a t} f (t)} = F (s - a)

Für

e^{3 t} (t^{2} + 4) : f (t) = (t^{2} + 4), a = 3

= L {(t^{2} + 4)} (s - 3)

L {(t^{2} + 4)} : \frac{2}{s ^{3}} + \frac{4}{s}

= \frac{2}{( s - 3 ) ^{3}} + \frac{4}{( s - 3 )}

= \frac{2}{( s - 3 ) ^{3}} + \frac{4}{s - 3}

Beliebte Beispiele

integral from 0 to 4 of 2sqrt(x)

\int_{0}^{4} 2 x d x

integral of θ^3sin(θ^2)

\int θ^{3} sin (θ^{2}) d θ

integral of x/((2x+1)^2)

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

integral from 1 to 2 of sin((npix)/2)

\int_{1}^{2} sin (\frac{nπ x}{2}) d x

derivative of sqrt(4(x+2^3))

\frac{d}{d x} (4 (x + 2)^{3})