integral of \sqrt[4]{x^3}+\sqrt[3]{x^8}

Lösung

\int 4 x^{3} + 3 x^{8} d x

\frac{4}{7} x^{\frac{7}{4}} + \frac{3}{11} x^{\frac{11}{3}} + C

Schritte zur Lösung

\int 4 x^{3} + 3 x^{8} 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 x^{3} d x + \int 3 x^{8} d x

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

\int 3 x^{8} d x = \frac{3}{11} x^{\frac{11}{3}}

= \frac{4}{7} x^{\frac{7}{4}} + \frac{3}{11} x^{\frac{11}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{4}{7} x^{\frac{7}{4}} + \frac{3}{11} x^{\frac{11}{3}} + C

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