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

Lösung

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

\frac{x ^{2}}{2} - ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{( x + 1 ) ( x - 1 )}{x} : x - \frac{1}{x}

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{2}}{2} - ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} - ln ∣ x ∣ + C

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