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Beliebt Rechnen >

integral of x^2\sqrt[3]{x+2x}

Lösung

\int x^{2} 3 x + 2 x d x

Lösung

33 (\frac{1}{3} x^{3} 3 x - \frac{1}{30} x^{\frac{10}{3}}) + C

Schritte zur Lösung

\int x^{2} 3 x + 2 x d x

3 x + 2 x = 33 3 x

= \int 33 x^{2} 3 x d x

Entferne die Konstante:

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

= 33 \cdot \int x^{2} 3 x d x

Wende die partielle Integration an

= 33 (\frac{1}{3} x^{3} 3 x - \int \frac{1}{9} x^{\frac{7}{3}} d x)

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

= 33 (\frac{1}{3} x^{3} 3 x - \frac{1}{30} x^{\frac{10}{3}})

Füge eine Konstante zur Lösung hinzu

= 33 (\frac{1}{3} x^{3} 3 x - \frac{1}{30} x^{\frac{10}{3}}) + C

Graph

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