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Beliebt >

integral of 7/8 xe^{x/(10)}

Lösung

\int \frac{7}{8} x e^{\frac{x}{10}} d x

Lösung

\frac{35}{4} e^{\frac{x}{10}} (x - 10) + C

Schritte zur Lösung

\int \frac{7}{8} x e^{\frac{x}{10}} d x

Entferne die Konstante:

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

= \frac{7}{8} \cdot \int x e^{\frac{x}{10}} d x

Wende die partielle Integration an

: 10 e^{\frac{x}{10}} x - \int 10 e^{\frac{x}{10}} d x

= \frac{7}{8} (10 e^{\frac{x}{10}} x - \int 10 e^{\frac{x}{10}} d x)

\int 10 e^{\frac{x}{10}} d x = 100 e^{\frac{x}{10}}

= \frac{7}{8} (10 e^{\frac{x}{10}} x - 100 e^{\frac{x}{10}})

Vereinfache

\frac{7}{8} (10 e^{\frac{x}{10}} x - 100 e^{\frac{x}{10}}) : \frac{35}{4} e^{\frac{x}{10}} (x - 10)

= \frac{35}{4} e^{\frac{x}{10}} (x - 10)

Füge eine Konstante zur Lösung hinzu

= \frac{35}{4} e^{\frac{x}{10}} (x - 10) + C

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