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Beliebt Rechnen >

integral of 1/2 xe^{x/6}

Lösung

\int \frac{1}{2} x e^{\frac{x}{6}} d x

Lösung

3 e^{\frac{x}{6}} (x - 6) + C

Schritte zur Lösung

\int \frac{1}{2} x e^{\frac{x}{6}} d x

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int x e^{\frac{x}{6}} d x

Wende die partielle Integration an

= \frac{1}{2} (6 e^{\frac{x}{6}} x - \int 6 e^{\frac{x}{6}} d x)

\int 6 e^{\frac{x}{6}} d x = 36 e^{\frac{x}{6}}

= \frac{1}{2} (6 e^{\frac{x}{6}} x - 36 e^{\frac{x}{6}})

Vereinfache

\frac{1}{2} (6 e^{\frac{x}{6}} x - 36 e^{\frac{x}{6}}) : 3 e^{\frac{x}{6}} (x - 6)

= 3 e^{\frac{x}{6}} (x - 6)

Füge eine Konstante zur Lösung hinzu

= 3 e^{\frac{x}{6}} (x - 6) + C

Graph

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