integral of (x-2)\sqrt[3]{x}

Lösung

\int (x - 2) 3 x d x

\frac{3}{7} x^{\frac{7}{3}} - \frac{3}{2} x^{\frac{4}{3}} + C

Schritte zur Lösung

\int (x - 2) 3 x d x

Multipliziere aus

(x - 2) 3 x : x^{\frac{4}{3}} - 2 3 x

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= \frac{3}{7} x^{\frac{7}{3}} - \frac{3}{2} x^{\frac{4}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{3}{7} x^{\frac{7}{3}} - \frac{3}{2} x^{\frac{4}{3}} + C

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