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Beliebt Rechnen >

integral of ln(r^2)r

Lösung

\int ln (r^{2}) r d r

Lösung

r^{2} ln (r) - \frac{r ^{2}}{2} + C

Schritte zur Lösung

\int ln (r^{2}) r d r

Wende die partielle Integration an

= \frac{1}{2} r^{2} ln (r^{2}) - \int r d r

\int r d r = \frac{r ^{2}}{2}

= \frac{1}{2} r^{2} ln (r^{2}) - \frac{r ^{2}}{2}

\frac{1}{2} r^{2} ln (r^{2}) = r^{2} ln (r)

= r^{2} ln (r) - \frac{r ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= r^{2} ln (r) - \frac{r ^{2}}{2} + C

Graph

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