integral t^2(e^t)^2

Lösung

integral

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

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

Schritte zur Lösung

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

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

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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