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Beliebt Rechnen >

integral of (1/x+1/(xln(x)))

Lösung

\int (\frac{1}{x} + \frac{1}{x ln ( x )}) d x

Lösung

ln ∣ x ∣ + ln ∣ ln (x) ∣ + C

Schritte zur Lösung

\int \frac{1}{x} + \frac{1}{x ln ( 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{1}{x} d x + \int \frac{1}{x ln ( x )} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{1}{x ln ( x )} d x = ln ∣ ln (x) ∣

= ln ∣ x ∣ + ln ∣ ln (x) ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ + ln ∣ ln (x) ∣ + C

Graph

Beliebte Beispiele

integral of-(cos(4x))/4

\int - \frac{cos ( 4 x )}{4} d x

integral of 2/(3-5x)

\int \frac{2}{3 - 5 x} d x

integral of (-3)/(3x^2+8x+4)

\int \frac{- 3}{3 x ^{2} + 8 x + 4} d x

integral of 3xln(8x)

\int 3 x ln (8 x) d x

integral of (x^6)/5

\int \frac{x ^{6}}{5} d x