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Beliebt Rechnen >

integral of t^2e^{4t}

Lösung

\int t^{2} e^{4 t} d t

Lösung

\frac{1}{4} e^{4 t} t^{2} - \frac{1}{32} (4 e^{4 t} t - e^{4 t}) + C

Schritte zur Lösung

\int t^{2} e^{4 t} d t

Wende die partielle Integration an

= \frac{1}{4} e^{4 t} t^{2} - \int \frac{1}{2} e^{4 t} t d t

\int \frac{1}{2} e^{4 t} t d t = \frac{1}{32} (4 e^{4 t} t - e^{4 t})

= \frac{1}{4} e^{4 t} t^{2} - \frac{1}{32} (4 e^{4 t} t - e^{4 t})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{4} e^{4 t} t^{2} - \frac{1}{32} (4 e^{4 t} t - e^{4 t}) + C

Graph

Beliebte Beispiele

integral of 9xe^{6x}

\int 9 x e^{6 x} d x

(dy)/(dx)=4+e^{y-4x+5}

\frac{d y}{d x} = 4 + e^{y - 4 x + 5}

derivative of e^{5-2x}

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

limit as x approaches-infinity of-8x

x \to - \infty lim (- 8 x)

integral from 0 to 4 of pi(4-y)

\int_{0}^{4} π (4 - y) d y