integral of (x^2-4x-6)/(x^2-6x)

Lösung

\int \frac{x ^{2} - 4 x - 6}{x ^{2} - 6 x} d x

ln x^{2} - 6 x + x + C

Schritte zur Lösung

\int \frac{x ^{2} - 4 x - 6}{x ^{2} - 6 x} d x

\frac{x ^{2} - 4 x - 6}{x ^{2} - 6 x} = \frac{2 x - 6}{x ^{2} - 6 x} + 1

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

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

\int 1 d x = x

= ln x^{2} - 6 x + x

Füge eine Konstante zur Lösung hinzu

= ln x^{2} - 6 x + x + C

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