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Beliebt Rechnen >

integral from 0 to 1 of (e^z+1)/(e^z+z)

Lösung

\int_{0}^{1} \frac{e ^{z} + 1}{e ^{z} + z} d z

Lösung

ln (e + 1)

+1

Dezimale

1.31326 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{e ^{z} + 1}{e ^{z} + z} d z

Wende U-Substitution an

= \int_{1}^{e + 1} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{e + 1}

Berechne die Grenzen:

ln (e + 1)

= ln (e + 1)

Graph

Beliebte Beispiele

(dy)/(dx)=40-3y

\frac{d y}{d x} = 40 - 3 y

integral of x^3cos(x^4+1)

\int x^{3} cos (x^{4} + 1) d x

integral of (6+x^9)^5x^8

\int (6 + x^{9})^{5} x^{8} d x

limit as h approaches infinity of (3h+2xh^2+x^2+h^3)/(4-3xh-2x^3h^3)

h \to \infty lim (\frac{3 h + 2 x h ^{2} + x ^{2} + h ^{3}}{4 - 3 x h - 2 x ^{3} h ^{3}})

limit as x approaches 3 of sin(1/(x-3))

x \to 3 lim (sin (\frac{1}{x - 3}))