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Beliebt Rechnen >

integral of (3x-1)^{1/8}

Lösung

\int (3 x - 1)^{\frac{1}{8}} d x

Lösung

\frac{8}{27} (3 x - 1)^{\frac{9}{8}} + C

Schritte zur Lösung

\int (3 x - 1)^{\frac{1}{8}} d x

Wende U-Substitution an

= \int \frac{u ^{\frac{1}{8}}}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int u^{\frac{1}{8}} d u

Wende die Potenzregel an

= \frac{1}{3} \cdot \frac{8}{9} u^{\frac{9}{8}}

Setze in

u = 3 x - 1

ein

= \frac{1}{3} \cdot \frac{8}{9} (3 x - 1)^{\frac{9}{8}}

Vereinfache

\frac{1}{3} \cdot \frac{8}{9} (3 x - 1)^{\frac{9}{8}} : \frac{8}{27} (3 x - 1)^{\frac{9}{8}}

= \frac{8}{27} (3 x - 1)^{\frac{9}{8}}

Füge eine Konstante zur Lösung hinzu

= \frac{8}{27} (3 x - 1)^{\frac{9}{8}} + C

Graph

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