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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{1}{ln ( x )} + ln ∣ ln (x) ∣ + C

Schritte zur Lösung

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

Vereinfache

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

Multipliziere aus

\frac{1 + ln ( x )}{x ln ^{2} ( x )} : \frac{1}{x ln ^{2} ( x )} + \frac{1}{x ln ( x )}

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

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

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

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

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{ln ( x )} + ln ∣ ln (x) ∣ + C

Graph

Beliebte Beispiele

integral of 6x^2(x^3-9)^3

\int 6 x^{2} (x^{3} - 9)^{3} d x

integral of (2x+1)(x^2+x+1)^5

\int (2 x + 1) (x^{2} + x + 1)^{5} d x

integral of (2x^2+2x-3)^{35}(2x+1)

\int (2 x^{2} + 2 x - 3)^{35} (2 x + 1) d x

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

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

integral of (3e^x)/(e^{2x)+9e^x+20}

\int \frac{3 e ^{x}}{e ^{2 x} + 9 e ^{x} + 20} d x