integral from 1 to e^4 of 1/(x(1+ln(x)))

Lösung

\int_{1}^{e^{4}} \frac{1}{x ( 1 + ln ( x ) )} d x

ln (5)

Dezimale

1.60943 \dots

Schritte zur Lösung

\int_{1}^{e^{4}} \frac{1}{x ( 1 + ln ( x ) )} d x

Wende U-Substitution an

= \int_{1}^{5} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{5}

Berechne die Grenzen:

ln (5)

= ln (5)

\int y^{2} \cdot cos (y) d y

\int \frac{5}{2 x - 2} d x

x \to 1 + lim (\frac{x}{ln ( x )})

x \to 3 lim (x^{2} + x - 5)

y^{^{''}} - (\frac{x}{x - 1}) y^{^{'}} + \frac{1}{x - 1} y = 0