integral of (12x^2-4x)/(x^2)

Lösung

\int \frac{12 x ^{2} - 4 x}{x ^{2}} d x

12 x - 4 ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{12 x ^{2} - 4 x}{x ^{2}} d x

Multipliziere aus

\frac{12 x ^{2} - 4 x}{x ^{2}} : 12 - \frac{4}{x}

= \int 12 - \frac{4}{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 12 d x - \int \frac{4}{x} d x

\int 12 d x = 12 x

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= 12 x - 4 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= 12 x - 4 ln ∣ x ∣ + C

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