What is the integral of rln((2r)/g) ?

The integral of rln((2r)/g) is 1/2 r^2ln((2r)/g)-(r^2)/4+C

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integral of rln((2r)/g)

\int r ln (\frac{2 r}{g}) d r

\frac{1}{2} r^{2} ln (\frac{2 r}{g}) - \frac{r ^{2}}{4} + C

Solution steps

\int r ln (\frac{2 r}{g}) d r

Apply Integration By Parts

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

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

\int \frac{r}{2} d r = \frac{r ^{2}}{4}

= \frac{1}{2} r^{2} ln (\frac{2 r}{g}) - \frac{r ^{2}}{4}

Add a constant to the solution

= \frac{1}{2} r^{2} ln (\frac{2 r}{g}) - \frac{r ^{2}}{4} + C

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What is the integral of rln((2r)/g) ?
The integral of rln((2r)/g) is 1/2 r^2ln((2r)/g)-(r^2)/4+C