integral from 0 to 1 of 2x^8ln(x)

Lösung

\int_{0}^{1} 2 x^{8} ln (x) d x

- \frac{2}{81}

Dezimale

- 0.02469 \dots

Schritte zur Lösung

\int_{0}^{1} 2 x^{8} ln (x) d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{1} x^{8} ln (x) d x

Wende die partielle Integration an

= 2 [\frac{1}{9} x^{9} ln (x) - \int \frac{x ^{8}}{9} d x]_{0}^{1}

\int \frac{x ^{8}}{9} d x = \frac{x ^{9}}{81}

= 2 [\frac{1}{9} x^{9} ln (x) - \frac{x ^{9}}{81}]_{0}^{1}

Berechne die Grenzen:

- \frac{1}{81}

= 2 (- \frac{1}{81})

Vereinfache

= - \frac{2}{81}

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