integral of \sqrt[7]{x}+\sqrt[8]{x}

Lösung

\int 7 x + 8 x d x

\frac{7}{8} x^{\frac{8}{7}} + \frac{8}{9} x^{\frac{9}{8}} + C

Schritte zur Lösung

\int 7 x + 8 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 7 x d x + \int 8 x d x

\int 7 x d x = \frac{7}{8} x^{\frac{8}{7}}

\int 8 x d x = \frac{8}{9} x^{\frac{9}{8}}

= \frac{7}{8} x^{\frac{8}{7}} + \frac{8}{9} x^{\frac{9}{8}}

Füge eine Konstante zur Lösung hinzu

= \frac{7}{8} x^{\frac{8}{7}} + \frac{8}{9} x^{\frac{9}{8}} + C

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