de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (ln(x)-2)/(xln(x)(ln(x)-1))

Lösung

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

Lösung

- ln ∣ ln (x) - 1 ∣ + 2 ln ∣ ln (x) ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{ln ( x ) - 2}{x ln ( x ) ( ln ( x ) - 1 )} : \frac{ln ( x )}{x ln ( x ) ( ln ( x ) - 1 )} - \frac{2}{x ln ( x ) ( ln ( x ) - 1 )}

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

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

\int \frac{2}{x ln ( x ) ( ln ( x ) - 1 )} d x = 2 (- ln ∣ ln (x) ∣ + ln ∣ ln (x) - 1 ∣)

= ln ∣ ln (x) - 1 ∣ - 2 (- ln ∣ ln (x) ∣ + ln ∣ ln (x) - 1 ∣)

Vereinfache

ln ∣ ln (x) - 1 ∣ - 2 (- ln ∣ ln (x) ∣ + ln ∣ ln (x) - 1 ∣) : - ln ∣ ln (x) - 1 ∣ + 2 ln ∣ ln (x) ∣

= - ln ∣ ln (x) - 1 ∣ + 2 ln ∣ ln (x) ∣

Füge eine Konstante zur Lösung hinzu

= - ln ∣ ln (x) - 1 ∣ + 2 ln ∣ ln (x) ∣ + C

Graph

Beliebte Beispiele

integral of sin(x)ln(x)cos(x)

\int sin (x) ln (x) cos (x) d x

laplacetransform e^{mt}

l a pl a ce t r an s f or m e^{m t}

integral of x/(sqrt(5+4x))

\int \frac{x}{5 + 4 x} d x

integral of x(x^2+3)^5

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

derivative of 3x^5-4x^4+9x-6

\frac{d}{d x} (3 x^{5} - 4 x^{4} + 9 x - 6)