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Beliebt Rechnen >

integral of x^8-4x^{-5}+6

Lösung

\int x^{8} - 4 x^{- 5} + 6 d x

Lösung

\frac{x ^{9}}{9} + \frac{1}{x ^{4}} + 6 x + C

Schritte zur Lösung

\int x^{8} - 4 x^{- 5} + 6 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^{8} d x - \int 4 x^{- 5} d x + \int 6 d x

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

\int 4 x^{- 5} d x = - \frac{1}{x ^{4}}

\int 6 d x = 6 x

= \frac{x ^{9}}{9} - (- \frac{1}{x ^{4}}) + 6 x

Vereinfache

= \frac{x ^{9}}{9} + \frac{1}{x ^{4}} + 6 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{9}}{9} + \frac{1}{x ^{4}} + 6 x + C

Graph

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