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Beliebt Rechnen >

integral from 1 to 3 of 4x^4ln(x)

Lösung

\int_{1}^{3} 4 x^{4} ln (x) d x

Lösung

4 (- \frac{242}{25} + \frac{243}{5} ln (3))

+1

Dezimale

174.85022 \dots

Schritte zur Lösung

\int_{1}^{3} 4 x^{4} ln (x) d x

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{3} x^{4} ln (x) d x

Wende die partielle Integration an

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

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

= 4 [\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}]_{1}^{3}

Berechne die Grenzen:

- \frac{242}{25} + \frac{243}{5} ln (3)

= 4 (- \frac{242}{25} + \frac{243}{5} ln (3))

Graph

Beliebte Beispiele

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