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

Lösung

\int (x^{3} + x) 3 x d x

\frac{6}{17} x^{\frac{17}{6}} + \frac{3}{7} x^{\frac{7}{3}} + C

Schritte zur Lösung

\int (x^{3} + x) 3 x d x

Multipliziere aus

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

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

\int 3 x x^{3} d x = \frac{6}{17} x^{\frac{17}{6}}

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

= \frac{6}{17} x^{\frac{17}{6}} + \frac{3}{7} x^{\frac{7}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{6}{17} x^{\frac{17}{6}} + \frac{3}{7} x^{\frac{7}{3}} + C

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