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Beliebt Rechnen >

integral of te^{t+2}

Lösung

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

Lösung

e^{2} (e^{t} t - e^{t}) + C

Schritte zur Lösung

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

t e^{t + 2} = e^{2} t e^{t}

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{2} \cdot \int t e^{t} d t

Wende die partielle Integration an

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

\int e^{t} d t = e^{t}

= e^{2} (e^{t} t - e^{t})

Füge eine Konstante zur Lösung hinzu

= e^{2} (e^{t} t - e^{t}) + C

Graph

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