integral of (7x+6)/(x^9)

Lösung

\int \frac{7 x + 6}{x ^{9}} d x

- \frac{1}{x ^{7}} - \frac{3}{4 x ^{8}} + C

Schritte zur Lösung

\int \frac{7 x + 6}{x ^{9}} d x

Multipliziere aus

\frac{7 x + 6}{x ^{9}} : \frac{7}{x ^{8}} + \frac{6}{x ^{9}}

= \int \frac{7}{x ^{8}} + \frac{6}{x ^{9}} 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 \frac{7}{x ^{8}} d x + \int \frac{6}{x ^{9}} d x

\int \frac{7}{x ^{8}} d x = - \frac{1}{x ^{7}}

\int \frac{6}{x ^{9}} d x = - \frac{3}{4 x ^{8}}

= - \frac{1}{x ^{7}} - \frac{3}{4 x ^{8}}

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{x ^{7}} - \frac{3}{4 x ^{8}} + C

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