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Beliebt Rechnen >

integral from 1/5 to 7 of 16xln(5x)

Lösung

\int_{\frac{1}{5}}^{7} 16 x ln (5 x) d x

Lösung

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

+1

Dezimale

1197.85644 \dots

Schritte zur Lösung

\int_{\frac{1}{5}}^{7} 16 x ln (5 x) d x

Entferne die Konstante:

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

= 16 \cdot \int_{\frac{1}{5}}^{7} x ln (5 x) d x

Wende die partielle Integration an

= 16 [\frac{1}{2} x^{2} ln (5 x) - \int \frac{x}{2} d x]_{\frac{1}{5}}^{7}

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

= 16 [\frac{1}{2} x^{2} ln (5 x) - \frac{x ^{2}}{4}]_{\frac{1}{5}}^{7}

Berechne die Grenzen:

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

= 16 (- \frac{306}{25} + \frac{49}{2} ln (35))

Graph

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