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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{3 e ^{4} - e ^{2}}{4}

+1

Dezimale

39.10134 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

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

2 \cdot \frac{x ^{2}}{4} = \frac{x ^{2}}{2}

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

Berechne die Grenzen:

\frac{3 e ^{4} - e ^{2}}{4}

= \frac{3 e ^{4} - e ^{2}}{4}

Graph

Beliebte Beispiele

integral from 0 to 1 of-2x+2

\int_{0}^{1} - 2 x + 2 d x

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\int_{- 1}^{0} x^{2} (4 x^{3} + 5)^{3} d x

integral from 1 to 3 of 2x-1

\int_{1}^{3} 2 x - 1 d x

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\int_{1}^{2} (x + 2) d x

integral from 0 to 3 of |3x-8|

\int_{0}^{3} ∣ 3 x - 8 ∣ d x