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Beliebt Rechnen >

integral from 0 to 8 of 1/(8-x)

Lösung

\int_{0}^{8} \frac{1}{8 - x} d x

Lösung

divergiert

Schritte zur Lösung

\int_{0}^{8} \frac{1}{8 - x} d x

Wende U-Substitution an

= \int_{8}^{0} - \frac{1}{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{8} - \frac{1}{u} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - (- \int_{0}^{8} \frac{1}{u} d u)

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- [ln ∣ u ∣]_{0}^{8})

Vereinfache

= [ln ∣ u ∣]_{0}^{8}

Berechne die Grenzen:

divergiert

= divergiert

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