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Beliebt Rechnen >

integral of \sqrt[3]{x}ln(6x)

Lösung

\int 3 x ln (6 x) d x

Lösung

\frac{3}{4} x^{\frac{4}{3}} ln (6 x) - \frac{9}{16} x^{\frac{4}{3}} + C

Schritte zur Lösung

\int 3 x ln (6 x) d x

Wende die partielle Integration an

= \frac{3}{4} x^{\frac{4}{3}} ln (6 x) - \int \frac{3}{4} x^{\frac{1}{3}} d x

\int \frac{3}{4} x^{\frac{1}{3}} d x = \frac{9}{16} x^{\frac{4}{3}}

= \frac{3}{4} x^{\frac{4}{3}} ln (6 x) - \frac{9}{16} x^{\frac{4}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{4} x^{\frac{4}{3}} ln (6 x) - \frac{9}{16} x^{\frac{4}{3}} + C

Graph

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