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Beliebt Rechnen >

integral of x(x-8)^{1/5}

Lösung

\int x (x - 8)^{\frac{1}{5}} d x

Lösung

\frac{5}{6} x (x - 8)^{\frac{6}{5}} - \frac{25}{66} (x - 8)^{\frac{11}{5}} + C

Schritte zur Lösung

\int x (x - 8)^{\frac{1}{5}} d x

Wende U-Substitution an

= \int (u + 8) u^{\frac{1}{5}} d u

Wende die partielle Integration an

= \frac{5}{6} u^{\frac{6}{5}} (u + 8) - \int \frac{5}{6} u^{\frac{6}{5}} d u

\int \frac{5}{6} u^{\frac{6}{5}} d u = \frac{25}{66} u^{\frac{11}{5}}

= \frac{5}{6} u^{\frac{6}{5}} (u + 8) - \frac{25}{66} u^{\frac{11}{5}}

Setze in

u = x - 8

ein

= \frac{5}{6} (x - 8)^{\frac{6}{5}} (x - 8 + 8) - \frac{25}{66} (x - 8)^{\frac{11}{5}}

Vereinfache

\frac{5}{6} (x - 8)^{\frac{6}{5}} (x - 8 + 8) - \frac{25}{66} (x - 8)^{\frac{11}{5}} : \frac{5}{6} x (x - 8)^{\frac{6}{5}} - \frac{25}{66} (x - 8)^{\frac{11}{5}}

= \frac{5}{6} x (x - 8)^{\frac{6}{5}} - \frac{25}{66} (x - 8)^{\frac{11}{5}}

Füge eine Konstante zur Lösung hinzu

= \frac{5}{6} x (x - 8)^{\frac{6}{5}} - \frac{25}{66} (x - 8)^{\frac{11}{5}} + C

Graph

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