integral of (x^9-1)/(x^4)

Lösung

\int \frac{x ^{9} - 1}{x ^{4}} d x

\frac{x ^{6}}{6} + \frac{1}{3 x ^{3}} + C

Schritte zur Lösung

\int \frac{x ^{9} - 1}{x ^{4}} d x

Multipliziere aus

\frac{x ^{9} - 1}{x ^{4}} : x^{5} - \frac{1}{x ^{4}}

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

\int x^{5} d x = \frac{x ^{6}}{6}

\int \frac{1}{x ^{4}} d x = - \frac{1}{3 x ^{3}}

= \frac{x ^{6}}{6} - (- \frac{1}{3 x ^{3}})

Vereinfache

= \frac{x ^{6}}{6} + \frac{1}{3 x ^{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{6}}{6} + \frac{1}{3 x ^{3}} + C

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