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Beliebt Rechnen >

integral of 1/(x-1)-1/(x+1)

Lösung

\int \frac{1}{x - 1} - \frac{1}{x + 1} d x

Lösung

ln ∣ x - 1 ∣ - ln ∣ x + 1 ∣ + C

Schritte zur Lösung

\int \frac{1}{x - 1} - \frac{1}{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{1}{x - 1} d x - \int \frac{1}{x + 1} d x

\int \frac{1}{x - 1} d x = ln ∣ x - 1 ∣

\int \frac{1}{x + 1} d x = ln ∣ x + 1 ∣

= ln ∣ x - 1 ∣ - ln ∣ x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x - 1 ∣ - ln ∣ x + 1 ∣ + C

Graph

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\int \frac{1}{x ^{2} - 15} d x

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\int (ln (x))^{12} \frac{1}{x} d x