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Beliebt Rechnen >

integral from 1/7 to 5 of 12xln(7x)

Lösung

\int_{\frac{1}{7}}^{5} 12 x ln (7 x) d x

Lösung

12 (- \frac{306}{49} + \frac{25}{2} ln (35))

+1

Dezimale

458.36343 \dots

Schritte zur Lösung

\int_{\frac{1}{7}}^{5} 12 x ln (7 x) d x

Entferne die Konstante:

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

= 12 \cdot \int_{\frac{1}{7}}^{5} x ln (7 x) d x

Wende die partielle Integration an

= 12 [\frac{1}{2} x^{2} ln (7 x) - \int \frac{x}{2} d x]_{\frac{1}{7}}^{5}

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

= 12 [\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4}]_{\frac{1}{7}}^{5}

Berechne die Grenzen:

- \frac{306}{49} + \frac{25}{2} ln (35)

= 12 (- \frac{306}{49} + \frac{25}{2} ln (35))

Graph

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