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

Lösung

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

\frac{3}{4}

Dezimale

0.75

Schritte zur Lösung

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

Wende die partielle Integration an

= [ln (x) (\frac{x ^{2}}{2} - x) - \int \frac{1}{2} (x - 2) d x]_{0}^{1}

\int \frac{1}{2} (x - 2) d x = \frac{x ^{2}}{4} - x

= [ln (x) (\frac{x ^{2}}{2} - x) - (\frac{x ^{2}}{4} - x)]_{0}^{1}

Vereinfache

[ln (x) (\frac{x ^{2}}{2} - x) - (\frac{x ^{2}}{4} - x)]_{0}^{1} : [\frac{1}{2} x^{2} ln (x) - x ln (x) - \frac{x ^{2}}{4} + x]_{0}^{1}

= [\frac{1}{2} x^{2} ln (x) - x ln (x) - \frac{x ^{2}}{4} + x]_{0}^{1}

Berechne die Grenzen:

\frac{3}{4}

= \frac{3}{4}

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