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Beliebt Rechnen >

integral of (x^6+8)/(x^5)

Lösung

\int \frac{x ^{6} + 8}{x ^{5}} d x

Lösung

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

Schritte zur Lösung

\int \frac{x ^{6} + 8}{x ^{5}} d x

Multipliziere aus

\frac{x ^{6} + 8}{x ^{5}} : x + \frac{8}{x ^{5}}

= \int x + \frac{8}{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 x d x + \int \frac{8}{x ^{5}} d x

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

\int \frac{8}{x ^{5}} d x = - \frac{2}{x ^{4}}

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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