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Beliebt Rechnen >

integral of (\sqrt[3]{x})^4

Lösung

\int (3 x)^{4} d x

Lösung

\frac{1}{2} x^{2} 3 x - \frac{1}{14} x^{\frac{7}{3}} + C

Schritte zur Lösung

\int (3 x)^{4} d x

Vereinfache

(3 x)^{4} : (3 x)^{3} 3 x

= \int (3 x)^{3} 3 x d x

(3 x)^{3} = x

= \int x 3 x d x

Wende die partielle Integration an

= \frac{1}{2} x^{2} 3 x - \int \frac{1}{6} x^{\frac{4}{3}} d x

\int \frac{1}{6} x^{\frac{4}{3}} d x = \frac{1}{14} x^{\frac{7}{3}}

= \frac{1}{2} x^{2} 3 x - \frac{1}{14} x^{\frac{7}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} 3 x - \frac{1}{14} x^{\frac{7}{3}} + C

Graph

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