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Beliebt Rechnen >

integral of (3x+1)(3x^2+2x)^{1/3}

Lösung

\int (3 x + 1) (3 x^{2} + 2 x)^{\frac{1}{3}} d x

Lösung

\frac{3}{8} (3 x^{2} + 2 x)^{\frac{4}{3}} + C

Schritte zur Lösung

\int (3 x + 1) (3 x^{2} + 2 x)^{\frac{1}{3}} d x

Wende U-Substitution an

= \int \frac{u ^{\frac{1}{3}}}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int u^{\frac{1}{3}} d u

Wende die Potenzregel an

= \frac{1}{2} \cdot \frac{3}{4} u^{\frac{4}{3}}

Setze in

u = 3 x^{2} + 2 x

ein

= \frac{1}{2} \cdot \frac{3}{4} (3 x^{2} + 2 x)^{\frac{4}{3}}

Vereinfache

\frac{1}{2} \cdot \frac{3}{4} (3 x^{2} + 2 x)^{\frac{4}{3}} : \frac{3}{8} (3 x^{2} + 2 x)^{\frac{4}{3}}

= \frac{3}{8} (3 x^{2} + 2 x)^{\frac{4}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{8} (3 x^{2} + 2 x)^{\frac{4}{3}} + C

Graph

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