integral from 2 to 5 of 1/(xln(x))

Lösung

\int_{2}^{5} \frac{1}{x ln ( x )} d x

ln (ln (5)) - ln (ln (2))

Dezimale

0.84239 \dots

Schritte zur Lösung

\int_{2}^{5} \frac{1}{x ln ( x )} d x

Wende U-Substitution an

= \int_{l n (2)}^{l n (5)} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{l n (2)}^{l n (5)}

Berechne die Grenzen:

ln (ln (5)) - ln (ln (2))

= ln (ln (5)) - ln (ln (2))

\int_{0}^{1} (t^{2} - t + \frac{1}{6})^{2} d t

\int_{2}^{\frac{1}{x}} sin^{4} (t) d t

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\int_{2}^{4} - 2 x + 4 d x

\int_{0}^{12} e^{- x} d x