What is the integral of ln(r^2)r ?

The integral of ln(r^2)r is r^2ln(r)-(r^2)/2+C

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integral of ln(r^2)r

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

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

Solution steps

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

Apply Integration By Parts

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

= \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}

Add a constant to the solution

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

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What is the integral of ln(r^2)r ?
The integral of ln(r^2)r is r^2ln(r)-(r^2)/2+C