integral of e^{2t+e^t}

Lösung

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

e^{e^{t} + t} - e^{e^{t}} + C

Schritte zur Lösung

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

Wende U-Substitution an

= \int e^{u} u d u

Wende die partielle Integration an

= e^{u} u - \int e^{u} d u

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

= e^{u} u - e^{u}

Setze in

u = e^{t}

ein

= e^{e^{t}} e^{t} - e^{e^{t}}

Wende Exponentenregel an:

a^{b} \cdot a^{c} = a^{b + c}

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

= e^{e^{t} + t} - e^{e^{t}}

Füge eine Konstante zur Lösung hinzu

= e^{e^{t} + t} - e^{e^{t}} + C