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Beliebt Rechnen >

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

Lösung

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

Lösung

ln (x) 1 + 2 ln (x) - \frac{1}{3} (2 ln (x) + 1)^{\frac{3}{2}} + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{1 + 2 ln ( x )}{x} d x = \frac{1}{3} (2 ln (x) + 1)^{\frac{3}{2}}

= ln (x) 1 + 2 ln (x) - \frac{1}{3} (2 ln (x) + 1)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= ln (x) 1 + 2 ln (x) - \frac{1}{3} (2 ln (x) + 1)^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

derivative y=ln(xsqrt(x^2-1))

d er i v a t i v e y = ln (x x^{2} - 1)

\frac{d y}{d x} = 2 y - 4

derivative of 8x^3-8

\frac{d}{d x} (8 x^{3} - 8)

derivative 5cot(x)

d er i v a t i v e 5 cot (x)

limit as x approaches-2 of 3x^4

x \to - 2 lim (3 x^{4})