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Beliebt Rechnen >

integral of e^{3x+e^x}

Lösung

\int e^{3 x + e^{x}} d x

Lösung

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

Schritte zur Lösung

\int e^{3 x + e^{x}} d x

Wende U-Substitution an

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

Wende die partielle Integration an

= u^{2} e^{u} - \int 2 u e^{u} d u

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

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

Setze in

u = e^{x}

ein

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

Vereinfache

(e^{x})^{2} e^{e^{x}} - 2 (e^{e^{x}} e^{x} - e^{e^{x}}) : e^{2 x + e^{x}} - 2 (e^{e^{x} + x} - e^{e^{x}})

= e^{2 x + e^{x}} - 2 (e^{e^{x} + x} - e^{e^{x}})

Füge eine Konstante zur Lösung hinzu

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

Graph

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