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Beliebt Rechnen >

integral of (arctan(ln(x)))/x

Lösung

\int \frac{arctan ( ln ( x ) )}{x} d x

Lösung

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

Schritte zur Lösung

\int \frac{arctan ( ln ( x ) )}{x} d x

Wende U-Substitution an

= \int arctan (u) d u

Wende die partielle Integration an

= u arctan (u) - \int \frac{u}{u ^{2} + 1} d u

\int \frac{u}{u ^{2} + 1} d u = \frac{1}{2} ln u^{2} + 1

= u arctan (u) - \frac{1}{2} ln u^{2} + 1

Setze in

u = ln (x)

ein

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

derivative f(x)=x^2sin(x^2+3)

d er i v a t i v e f (x) = x^{2} sin (x^{2} + 3)

derivative g(t)=tsqrt(t)\sqrt[3]{t}

d er i v a t i v e g (t) = t t 3 t

integral of (sqrt(x^2-9))/(x^2)

\int \frac{x ^{2} - 9}{x ^{2}} d x

y^{''}-(6/x)y^'-(4/(x^2))y=0

y^{^{''}} - (\frac{6}{x}) y^{^{'}} - (\frac{4}{x ^{2}}) y = 0

d/(da)((pi(9a^2+6a+1))/(36a))

\frac{d}{d a} (\frac{π ( 9 a ^{2} + 6 a + 1 )}{36 a})