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Beliebt Rechnen >

integral of (x^2-1)/x

Lösung

\int \frac{x ^{2} - 1}{x} d x

Lösung

\frac{x ^{2}}{2} - ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{x ^{2} - 1}{x} d x

Multipliziere aus

\frac{x ^{2} - 1}{x} : x - \frac{1}{x}

= \int x - \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 x d x - \int \frac{1}{x} d x

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

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{2}}{2} - ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} - ln ∣ x ∣ + C

Graph

Beliebte Beispiele

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

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

maclaurin (1/3)^x

ma c l a u r in (\frac{1}{3})^{x}

integral from 0 to 1 of sqrt(2x+1)

\int_{0}^{1} 2 x + 1 d x

limit as x approaches infinity+of sqrt(25x^4+9x)-5x^2

x \to \infty + lim (25 x^{4} + 9 x - 5 x^{2})

derivative of 2^e

\frac{d}{d x} (2^{e})