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Beliebt Rechnen >

integral of 6t^2*\sqrt[3]{t}

Lösung

\int 6 t^{2} \cdot 3 t d t

Lösung

6 (\frac{1}{3} t^{3} 3 t - \frac{1}{30} t^{\frac{10}{3}}) + C

Schritte zur Lösung

\int 6 t^{2} 3 t d t

Entferne die Konstante:

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

= 6 \cdot \int t^{2} 3 t d t

Wende die partielle Integration an

= 6 (\frac{1}{3} t^{3} 3 t - \int \frac{1}{9} t^{\frac{7}{3}} d t)

\int \frac{1}{9} t^{\frac{7}{3}} d t = \frac{1}{30} t^{\frac{10}{3}}

= 6 (\frac{1}{3} t^{3} 3 t - \frac{1}{30} t^{\frac{10}{3}})

Füge eine Konstante zur Lösung hinzu

= 6 (\frac{1}{3} t^{3} 3 t - \frac{1}{30} t^{\frac{10}{3}}) + C

Graph

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