integral from 1 to e^6 of 1/(x(1+ln(x)))

Lösung

\int_{1}^{e^{6}} \frac{1}{x ( 1 + ln ( x ) )} d x

ln (7)

Dezimale

1.94591 \dots

Schritte zur Lösung

\int_{1}^{e^{6}} \frac{1}{x ( 1 + ln ( x ) )} d x

Wende U-Substitution an

= \int_{1}^{7} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{7}

Berechne die Grenzen:

ln (7)

= ln (7)

\int_{0}^{1} 2 x (1 - x^{2})^{4} d x

\int_{- 1}^{2} (3 x^{2} - 2 x) d x

\int_{- 1}^{1} x^{6} d x

\int_{0}^{2} - x^{2} + 3 x - 2 d x

\int_{- 2}^{2} ∣ x + 1 ∣ d x