integral from 2 to 3 of x^2ln(x)

Lösung

\int_{2}^{3} x^{2} ln (x) d x

9 ln (3) - \frac{19}{9} - \frac{8}{3} ln (2)

Dezimale

5.92800 \dots

Schritte zur Lösung

\int_{2}^{3} x^{2} ln (x) d x

Wende die partielle Integration an

= [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{2}^{3}

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= [\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}]_{2}^{3}

Berechne die Grenzen:

9 ln (3) - \frac{19}{9} - \frac{8}{3} ln (2)

= 9 ln (3) - \frac{19}{9} - \frac{8}{3} ln (2)

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