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

Lösung

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

ln ln^{2} (x) + 1 + ln (x) + C

Schritte zur Lösung

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

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

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

= ln u^{2} + 1 + u

Setze in

u = ln (x)

ein

= ln ln^{2} (x) + 1 + ln (x)

Füge eine Konstante zur Lösung hinzu

= ln ln^{2} (x) + 1 + ln (x) + C

\int \frac{4 x}{( x ^{2} + 1 ) ^{2}} d x

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