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Beliebt Rechnen >

integral of xe^{8x}

Lösung

\int x e^{8 x} d x

Lösung

\frac{1}{64} (e^{8 x} \cdot 8 x - e^{8 x}) + C

Schritte zur Lösung

\int x e^{8 x} d x

Wende U-Substitution an

= \int \frac{e ^{u} u}{64} d u

Entferne die Konstante:

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

= \frac{1}{64} \cdot \int e^{u} u d u

Wende die partielle Integration an

= \frac{1}{64} (e^{u} u - \int e^{u} d u)

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

= \frac{1}{64} (e^{u} u - e^{u})

Setze in

u = 8 x

ein

= \frac{1}{64} (e^{8 x} \cdot 8 x - e^{8 x})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{64} (e^{8 x} \cdot 8 x - e^{8 x}) + C

Graph

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