integral from 0 to 1 of (8ln(x))

Lösung

\int_{0}^{1} (8 ln (x)) d x

- 8

Schritte zur Lösung

\int_{0}^{1} 8 ln (x) d x

Entferne die Konstante:

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

= 8 \cdot \int_{0}^{1} ln (x) d x

Wende die partielle Integration an

= 8 [x ln (x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= 8 [x ln (x) - x]_{0}^{1}

Berechne die Grenzen:

- 1

= 8 (- 1)

Vereinfache

= - 8

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