integral from 1 to e^8 of 1/(x(1+ln(x)))

Lösung

\int_{1}^{e^{8}} \frac{1}{x ( 1 + ln ( x ) )} d x

2 ln (3)

Dezimale

2.19722 \dots

Schritte zur Lösung

\int_{1}^{e^{8}} \frac{1}{x ( 1 + ln ( x ) )} d x

Wende U-Substitution an

= \int_{1}^{9} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{9}

Berechne die Grenzen:

2 ln (3)

= 2 ln (3)

\int_{- 4}^{4} ∣ x + 2 ∣ d x

\int_{3}^{7} 8 d x

\int_{0}^{1} x cos (\frac{nπ x}{1}) d x

\int_{0}^{2 π} sin (t) + cos (t) d t

\int_{5}^{6} (\frac{5}{x ^{2}} - 1) d x