integral of (x^{-3}-6x^{-2}+10)

Lösung

\int (x^{- 3} - 6 x^{- 2} + 10) d x

- \frac{1}{2 x ^{2}} + \frac{6}{x} + 10 x + C

Schritte zur Lösung

\int x^{- 3} - 6 x^{- 2} + 10 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^{- 3} d x - \int 6 x^{- 2} d x + \int 10 d x

\int x^{- 3} d x = - \frac{1}{2 x ^{2}}

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

\int 10 d x = 10 x

= - \frac{1}{2 x ^{2}} - (- \frac{6}{x}) + 10 x

Vereinfache

= - \frac{1}{2 x ^{2}} + \frac{6}{x} + 10 x

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2 x ^{2}} + \frac{6}{x} + 10 x + C

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