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Beliebt Rechnen >

integral from 1 to e^3 of x^3ln(x)

Lösung

\int_{1}^{e^{3}} x^{3} ln (x) d x

Lösung

\frac{11 e ^{12} + 1}{16}

+1

Dezimale

111893.98160 \dots

Schritte zur Lösung

\int_{1}^{e^{3}} x^{3} ln (x) d x

Wende die partielle Integration an

= [\frac{1}{4} (x^{4} ln (x) - 4 \cdot \int \frac{x ^{3}}{4} d x)]_{1}^{e^{3}}

\int \frac{x ^{3}}{4} d x = \frac{x ^{4}}{16}

= [\frac{1}{4} (x^{4} ln (x) - 4 \cdot \frac{x ^{4}}{16})]_{1}^{e^{3}}

4 \cdot \frac{x ^{4}}{16} = \frac{x ^{4}}{4}

= [\frac{1}{4} (x^{4} ln (x) - \frac{x ^{4}}{4})]_{1}^{e^{3}}

Berechne die Grenzen:

\frac{11 e ^{12}}{16} + \frac{1}{16}

= \frac{11 e ^{12}}{16} + \frac{1}{16}

Vereinfache

= \frac{11 e ^{12} + 1}{16}

Graph

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