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Beliebt Rechnen >

integral of (3x^2+2x+1)/x

Lösung

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

Lösung

\frac{3 x ^{2}}{2} + 2 x + ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

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

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

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

\int 2 d x = 2 x

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{3 x ^{2}}{2} + 2 x + ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{3 x ^{2}}{2} + 2 x + ln ∣ x ∣ + C

Graph

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