integral from 0 to 1 of (e^z+5)/(e^z+5z)

Lösung

\int_{0}^{1} \frac{e ^{z} + 5}{e ^{z} + 5 z} d z

ln (e + 5)

Dezimale

2.04359 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{e ^{z} + 5}{e ^{z} + 5 z} d z

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{1}^{e + 5}

Berechne die Grenzen:

ln (e + 5)

= ln (e + 5)

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