integral of x^{7/2}ln(x)

Lösung

\int x^{\frac{7}{2}} ln (x) d x

\frac{2}{9} x^{\frac{9}{2}} ln (x) - \frac{4}{81} x^{\frac{9}{2}} + C

Schritte zur Lösung

\int x^{\frac{7}{2}} ln (x) d x

Wende die partielle Integration an

= \frac{2}{9} x^{\frac{9}{2}} ln (x) - \int \frac{2}{9} x^{\frac{7}{2}} d x

\int \frac{2}{9} x^{\frac{7}{2}} d x = \frac{4}{81} x^{\frac{9}{2}}

= \frac{2}{9} x^{\frac{9}{2}} ln (x) - \frac{4}{81} x^{\frac{9}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{9} x^{\frac{9}{2}} ln (x) - \frac{4}{81} x^{\frac{9}{2}} + C

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