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Beliebt Rechnen >

integral from 1 to 5 of 6xln(x)

Lösung

\int_{1}^{5} 6 x ln (x) d x

Lösung

6 (- 6 + \frac{25}{2} ln (5))

+1

Dezimale

84.70784 \dots

Schritte zur Lösung

\int_{1}^{5} 6 x ln (x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int_{1}^{5} x ln (x) d x

Wende die partielle Integration an

= 6 [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{1}^{5}

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

= 6 [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{1}^{5}

Berechne die Grenzen:

- 6 + \frac{25}{2} ln (5)

= 6 (- 6 + \frac{25}{2} ln (5))

Graph

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