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

Lösung

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

- ln ∣ - t + 1 ∣

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{1 - t} - \frac{1}{u} d u

Entferne die Konstante:

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

= - \int_{1}^{1 - t} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= - [ln ∣ u ∣]_{1}^{1 - t}

Berechne die Grenzen:

ln ∣ - t + 1 ∣

= - ln ∣ - t + 1 ∣

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