integral from 1 to 10 of x^2ln(x)

Lösung

\int_{1}^{10} x^{2} ln (x) d x

- 111 + \frac{1000}{3} ln (10)

Dezimale

656.52836 \dots

Schritte zur Lösung

\int_{1}^{10} 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]_{1}^{10}

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

= [\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}]_{1}^{10}

Berechne die Grenzen:

- 111 + \frac{1000}{3} ln (10)

= - 111 + \frac{1000}{3} ln (10)

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