integral of (x+3)/(x^2)

Lösung

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

ln ∣ x ∣ - \frac{3}{x} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x + 3}{x ^{2}} : \frac{1}{x} + \frac{3}{x ^{2}}

= \int \frac{1}{x} + \frac{3}{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{1}{x} d x + \int \frac{3}{x ^{2}} d x

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ - \frac{3}{x}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - \frac{3}{x} + C

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