integral from a to b of 1/(1-x)

Lösung

\int_{a}^{b} \frac{1}{1 - x} d x

- ln ∣ 1 - b ∣ + ln ∣ 1 - a ∣

Schritte zur Lösung

\int_{a}^{b} \frac{1}{1 - x} d x

Wende U-Substitution an

= \int_{1 - a}^{1 - b} - \frac{1}{u} d u

Entferne die Konstante:

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

= - \int_{1 - a}^{1 - b} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= - [ln ∣ u ∣]_{1 - a}^{1 - b}

Berechne die Grenzen:

ln ∣ 1 - b ∣ - ln ∣ 1 - a ∣

= - (ln ∣ 1 - b ∣ - ln ∣ 1 - a ∣)

Vereinfache

= - ln ∣ 1 - b ∣ + ln ∣ 1 - a ∣

\int_{- 3}^{5} 2 d x

\int_{0}^{5} (2 x + 3)^{2} d x

\int_{0}^{9} y + 14 d y

\int_{0}^{17} 85 - 4 x d x

\int_{0}^{5} r^{2} d r