integral from 1 to e of x^9ln(x)

Lösung

\int_{1}^{e} x^{9} ln (x) d x

\frac{9 e ^{10} + 1}{100}

Dezimale

1982.39192 \dots

Schritte zur Lösung

\int_{1}^{e} x^{9} ln (x) d x

Wende die partielle Integration an

= [\frac{1}{10} (x^{10} ln (x) - 10 \cdot \int \frac{x ^{9}}{10} d x)]_{1}^{e}

\int \frac{x ^{9}}{10} d x = \frac{x ^{10}}{100}

= [\frac{1}{10} (x^{10} ln (x) - 10 \cdot \frac{x ^{10}}{100})]_{1}^{e}

10 \cdot \frac{x ^{10}}{100} = \frac{x ^{10}}{10}

= [\frac{1}{10} (x^{10} ln (x) - \frac{x ^{10}}{10})]_{1}^{e}

Berechne die Grenzen:

\frac{9 e ^{10}}{100} + \frac{1}{100}

= \frac{9 e ^{10}}{100} + \frac{1}{100}

Vereinfache

= \frac{9 e ^{10} + 1}{100}

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