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Beliebt Rechnen >

integral of 1/(x^7)-2/(x^6)+9x+8

Lösung

\int \frac{1}{x ^{7}} - \frac{2}{x ^{6}} + 9 x + 8 d x

Lösung

- \frac{1}{6 x ^{6}} + \frac{2}{5 x ^{5}} + \frac{9 x ^{2}}{2} + 8 x + C

Schritte zur Lösung

\int \frac{1}{x ^{7}} - \frac{2}{x ^{6}} + 9 x + 8 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{1}{x ^{7}} d x - \int \frac{2}{x ^{6}} d x + \int 9 x d x + \int 8 d x

\int \frac{1}{x ^{7}} d x = - \frac{1}{6 x ^{6}}

\int \frac{2}{x ^{6}} d x = - \frac{2}{5 x ^{5}}

\int 9 x d x = \frac{9 x ^{2}}{2}

\int 8 d x = 8 x

= - \frac{1}{6 x ^{6}} - (- \frac{2}{5 x ^{5}}) + \frac{9 x ^{2}}{2} + 8 x

Vereinfache

= - \frac{1}{6 x ^{6}} + \frac{2}{5 x ^{5}} + \frac{9 x ^{2}}{2} + 8 x

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{6 x ^{6}} + \frac{2}{5 x ^{5}} + \frac{9 x ^{2}}{2} + 8 x + C

Graph

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