laplacetransform f(t)=e^{t+7}

Lösung

laplace transformation

f (t) = e^{t + 7}

\frac{e ^{7}}{s - 1}

Schritte zur Lösung

L {e^{t + 7}}

Verwende die konstante Multiplikationseigenschaft der Laplace-Transformation:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= e^{7} L {e^{t}}

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

= e^{7} \frac{1}{s - 1}

Fasse

e^{7} \frac{1}{s - 1}

zusammen:

\frac{e ^{7}}{s - 1}

= \frac{e ^{7}}{s - 1}

l a pl a ce t r an s f or m 3 y

\frac{d}{d x} (\frac{1}{3 x ^{2}} - \frac{5}{2 x} + 8 x - 6)

\frac{d}{d x} (2 cos (- x))

in v erse l a pl a ce \frac{( x )}{( x + 2 ) ( x - 3 )}

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