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

Lösung

\int (4 - x) 3 x d x

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

Schritte zur Lösung

\int (4 - x) 3 x d x

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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