What is the integral of rln(r) ?

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

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integral of rln(r)

\int r ln (r) d r

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

Solution steps

\int r ln (r) d r

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

x \to 1 lim (\frac{x ^{8} - 1}{x - 1})

n = 1 \sum \infty \frac{( 3 ^{n - 1} )}{9 ^{n}}

\frac{d}{d x} (4 x 16 - x^{2})

\int_{1}^{2} 2 x x^{2} + 1 d x

n = 3 \sum \infty \frac{1}{3 ^{n}}

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