integral from 3 to 5 of xln(x)

Lösung

\int_{3}^{5} x ln (x) d x

- 4 + \frac{25 ln ( 5 ) - 9 ln ( 3 )}{2}

Dezimale

11.17421 \dots

Schritte zur Lösung

\int_{3}^{5} x ln (x) d x

Wende die partielle Integration an

= [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{3}^{5}

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

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{3}^{5}

Berechne die Grenzen:

- 4 + \frac{25 ln ( 5 ) - 9 ln ( 3 )}{2}

= - 4 + \frac{25 ln ( 5 ) - 9 ln ( 3 )}{2}