integral of (x-2/x)(x+2/x)

Lösung

\int (x - \frac{2}{x}) (x + \frac{2}{x}) d x

\frac{x ^{3}}{3} + \frac{4}{x} + C

Schritte zur Lösung

\int (x - \frac{2}{x}) (x + \frac{2}{x}) d x

Multipliziere aus

(x - \frac{2}{x}) (x + \frac{2}{x}) : x^{2} - \frac{4}{x ^{2}}

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

\int x^{2} d x = \frac{x ^{3}}{3}

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

= \frac{x ^{3}}{3} - (- \frac{4}{x})

Vereinfache

= \frac{x ^{3}}{3} + \frac{4}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + \frac{4}{x} + C

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