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

Lösung

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

\frac{5 e ^{6} - 2 e ^{3}}{9}

Dezimale

219.66365 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

3 \cdot \frac{x ^{3}}{9} = \frac{x ^{3}}{3}

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

Berechne die Grenzen:

\frac{5 e ^{6} - 2 e ^{3}}{9}

= \frac{5 e ^{6} - 2 e ^{3}}{9}

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