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Beliebt Rechnen >

integral of t^2e^{9t}

Lösung

\int t^{2} e^{9 t} d t

Lösung

\frac{1}{9} e^{9 t} t^{2} - \frac{2}{729} (9 e^{9 t} t - e^{9 t}) + C

Schritte zur Lösung

\int t^{2} e^{9 t} d t

Wende die partielle Integration an

= \frac{1}{9} e^{9 t} t^{2} - \int \frac{2}{9} e^{9 t} t d t

\int \frac{2}{9} e^{9 t} t d t = \frac{2}{729} (9 e^{9 t} t - e^{9 t})

= \frac{1}{9} e^{9 t} t^{2} - \frac{2}{729} (9 e^{9 t} t - e^{9 t})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{9} e^{9 t} t^{2} - \frac{2}{729} (9 e^{9 t} t - e^{9 t}) + C

Graph

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