integral of (2\sqrt[3]{x}-7sqrt(x^5))

Lösung

\int (2 3 x - 7 x^{5}) d x

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

Schritte zur Lösung

\int 2 3 x - 7 x^{5} 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 2 3 x d x - \int 7 x^{5} d x

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

\int 7 x^{5} d x = 2 x^{\frac{7}{2}}

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

Füge eine Konstante zur Lösung hinzu

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

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