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

Lösung

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

- \frac{1023}{25} + \frac{2048}{5} ln (2)

Dezimale

242.99308 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Berechne die Grenzen:

- \frac{1023}{25} + \frac{2048}{5} ln (2)

= - \frac{1023}{25} + \frac{2048}{5} ln (2)

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