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

Lösung

\int 3 x (x + 4) d x

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

Schritte zur Lösung

\int 3 x (x + 4) d x

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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