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Beliebt Rechnen >

integral of x+x^{11}+x^{-11}

Lösung

\int x + x^{11} + x^{- 11} d x

Lösung

\frac{x ^{2}}{2} + \frac{x ^{12}}{12} - \frac{1}{10 x ^{10}} + C

Schritte zur Lösung

\int x + x^{11} + x^{- 11} 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 x^{11} d x + \int x^{- 11} d x

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

\int x^{11} d x = \frac{x ^{12}}{12}

\int x^{- 11} d x = - \frac{1}{10 x ^{10}}

= \frac{x ^{2}}{2} + \frac{x ^{12}}{12} - \frac{1}{10 x ^{10}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + \frac{x ^{12}}{12} - \frac{1}{10 x ^{10}} + C

Graph

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