integral from 1 to 5 of 1/(x-p)

Lösung

\int_{1}^{5} \frac{1}{x - p} d x

ln ∣ - p + 5 ∣ - ln ∣ - p + 1 ∣

Schritte zur Lösung

\int_{1}^{5} \frac{1}{x - p} d x

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{- p + 1}^{- p + 5}

Berechne die Grenzen:

ln ∣ - p + 5 ∣ - ln ∣ - p + 1 ∣

= ln ∣ - p + 5 ∣ - ln ∣ - p + 1 ∣