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Beliebt Rechnen >

integral of x/((x^2-5)^{1/7)}

Lösung

\int \frac{x}{( x ^{2} - 5 ) ^{\frac{1}{7}}} d x

Lösung

\frac{7}{12} (x^{2} - 5)^{\frac{6}{7}} + C

Schritte zur Lösung

\int \frac{x}{( x ^{2} - 5 ) ^{\frac{1}{7}}} d x

Wende U-Substitution an

= \int \frac{1}{2 ( u - 5 ) ^{\frac{1}{7}}} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int \frac{1}{( u - 5 ) ^{\frac{1}{7}}} d u

Wende U-Substitution an

= \frac{1}{2} \cdot \int \frac{1}{v ^{\frac{1}{7}}} d v

Wende die Potenzregel an

= \frac{1}{2} \cdot \frac{7}{6} v^{\frac{6}{7}}

Ersetze zurück

= \frac{1}{2} \cdot \frac{7}{6} (x^{2} - 5)^{\frac{6}{7}}

Vereinfache

\frac{1}{2} \cdot \frac{7}{6} (x^{2} - 5)^{\frac{6}{7}} : \frac{7}{12} (x^{2} - 5)^{\frac{6}{7}}

= \frac{7}{12} (x^{2} - 5)^{\frac{6}{7}}

Füge eine Konstante zur Lösung hinzu

= \frac{7}{12} (x^{2} - 5)^{\frac{6}{7}} + C

Graph

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