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

Lösung

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

\frac{3 e ^{4} + 1}{16}

Dezimale

10.29965 \dots

Schritte zur Lösung

\int_{1}^{e} 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}

\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}

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

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

Berechne die Grenzen:

\frac{3 e ^{4}}{16} + \frac{1}{16}

= \frac{3 e ^{4}}{16} + \frac{1}{16}

Vereinfache

= \frac{3 e ^{4} + 1}{16}