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Beliebt Rechnen >

integral of (ln|x|)/x

Lösung

\int \frac{ln ∣ x ∣}{x} d x

Lösung

\frac{ln ∣ x ∣ ^{2}}{2} + C

Schritte zur Lösung

\int \frac{ln ∣ x ∣}{x} d x

\frac{ln ∣ x ∣}{x} = ln ∣ x ∣ \frac{1}{x}

= \int ln ∣ x ∣ \frac{1}{x} d x

Wende U-Substitution an

= \int u d u

Wende die Potenzregel an

= \frac{u ^{2}}{2}

Setze in

u = ln ∣ x ∣

ein

= \frac{ln ∣ x ∣ ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{ln ∣ x ∣ ^{2}}{2} + C

Graph

Beliebte Beispiele

derivative f(t)=(3t-1)^4(2t+1)^{-3}

d er i v a t i v e f (t) = (3 t - 1)^{4} (2 t + 1)^{- 3}

limit as x approaches 0 of (tan(kx))/x

x \to 0 lim (\frac{tan ( k x )}{x})

integral of z^3e^z

\int z^{3} e^{z} d z

derivative of arctan(ln(x^2))

\frac{d}{d x} (arctan (ln (x^{2})))

derivative of ln(sqrt(2x))

\frac{d}{d x} (ln (2 x))