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Beliebt Rechnen >

integral of (x/2-2/x)

Lösung

\int (\frac{x}{2} - \frac{2}{x}) d x

Lösung

\frac{x ^{2}}{4} - 2 ln ∣ x ∣ + C

Schritte zur Lösung

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

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{x ^{2}}{4} - 2 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{4} - 2 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of sqrt(x^6)

\int x^{6} d x

integral of (4x-5)(2x+1)

\int (4 x - 5) (2 x + 1) d x

integral of x^2(x^3-4)^5

\int x^{2} (x^{3} - 4)^{5} d x

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

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

integral of 7/(5xsqrt(25x^2-16))

\int \frac{7}{5 x 25 x ^{2} - 16} d x