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Beliebt Rechnen >

integral of (x^2-2x-5)/(x^2+1)

Lösung

\int \frac{x ^{2} - 2 x - 5}{x ^{2} + 1} d x

Lösung

- ln x^{2} + 1 - 6 arctan (x) + x + C

Schritte zur Lösung

\int \frac{x ^{2} - 2 x - 5}{x ^{2} + 1} d x

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

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

\int \frac{- 2 x - 6}{x ^{2} + 1} d x = - ln x^{2} + 1 - 6 arctan (x)

\int 1 d x = x

= - ln x^{2} + 1 - 6 arctan (x) + x

Füge eine Konstante zur Lösung hinzu

= - ln x^{2} + 1 - 6 arctan (x) + x + C

Graph

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