integral of x^nln(x)

Lösung

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

\frac{1}{n + 1} x^{n + 1} ln (x) - \frac{x ^{n + 1}}{( n + 1 ) ^{2}} + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{1}{n + 1} x^{n + 1} ln (x) - \int \frac{x ^{n}}{n + 1} d x

\int \frac{x ^{n}}{n + 1} d x = \frac{x ^{n + 1}}{( n + 1 ) ^{2}}

= \frac{1}{n + 1} x^{n + 1} ln (x) - \frac{x ^{n + 1}}{( n + 1 ) ^{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{n + 1} x^{n + 1} ln (x) - \frac{x ^{n + 1}}{( n + 1 ) ^{2}} + C

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