integral of x^{1000}ln(x)

Lösung

\int x^{1000} ln (x) d x

\frac{1}{1001} x^{1001} ln (x) - \frac{x ^{1001}}{1002001} + C

Schritte zur Lösung

\int x^{1000} ln (x) d x

Wende die partielle Integration an

= \frac{1}{1001} x^{1001} ln (x) - \int \frac{x ^{1000}}{1001} d x

\int \frac{x ^{1000}}{1001} d x = \frac{x ^{1001}}{1002001}

= \frac{1}{1001} x^{1001} ln (x) - \frac{x ^{1001}}{1002001}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{1001} x^{1001} ln (x) - \frac{x ^{1001}}{1002001} + C

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