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

Lösung

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

2 ln ∣ x ∣ + \frac{2}{x} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{2 x - 2}{x ^{2}} : \frac{2}{x} - \frac{2}{x ^{2}}

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= 2 ln ∣ x ∣ - (- \frac{2}{x})

Vereinfache

= 2 ln ∣ x ∣ + \frac{2}{x}

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x ∣ + \frac{2}{x} + C

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