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

Lösung

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

- \frac{1}{2} ln x^{2} + 9 - \frac{8}{3} arctan (\frac{x}{3}) + C

Schritte zur Lösung

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

Multipliziere aus

\frac{- x - 8}{x ^{2} + 9} : - \frac{x}{x ^{2} + 9} - \frac{8}{x ^{2} + 9}

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

\int \frac{x}{x ^{2} + 9} d x = \frac{1}{2} ln x^{2} + 9

\int \frac{8}{x ^{2} + 9} d x = \frac{8}{3} arctan (\frac{x}{3})

= - \frac{1}{2} ln x^{2} + 9 - \frac{8}{3} arctan (\frac{x}{3})

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} ln x^{2} + 9 - \frac{8}{3} arctan (\frac{x}{3}) + C

\int 15 arctan (x) d x

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