integral of x\sqrt[3]{5-6x^2}

Lösung

\int x 3 5 - 6 x^{2} d x

- \frac{1}{16} (5 - 6 x^{2})^{\frac{4}{3}} + C

Schritte zur Lösung

\int x 3 5 - 6 x^{2} d x

Wende U-Substitution an

= \int - \frac{3 u}{12} d u

Entferne die Konstante:

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

= - \frac{1}{12} \cdot \int 3 u d u

Wende die Potenzregel an

= - \frac{1}{12} \cdot \frac{3}{4} u^{\frac{4}{3}}

Setze in

u = 5 - 6 x^{2}

ein

= - \frac{1}{12} \cdot \frac{3}{4} (5 - 6 x^{2})^{\frac{4}{3}}

Vereinfache

- \frac{1}{12} \cdot \frac{3}{4} (5 - 6 x^{2})^{\frac{4}{3}} : - \frac{1}{16} (5 - 6 x^{2})^{\frac{4}{3}}

= - \frac{1}{16} (5 - 6 x^{2})^{\frac{4}{3}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{16} (5 - 6 x^{2})^{\frac{4}{3}} + C

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