What is the integral from 1 to 5 of 5r^2ln(r) ?

The integral from 1 to 5 of 5r^2ln(r) is 5(-124/9+125/3 ln(5))

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integral from 1 to 5 of 5r^2ln(r)

\int_{1}^{5} 5 r^{2} ln (r) d r

5 (- \frac{124}{9} + \frac{125}{3} ln (5))

Decimal Notation

266.41067 \dots

Solution steps

\int_{1}^{5} 5 r^{2} ln (r) d r

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int_{1}^{5} r^{2} ln (r) d r

Apply Integration By Parts

: [\frac{1}{3} r^{3} ln (r) - \int \frac{r ^{2}}{3} d r]_{1}^{5}

= 5 [\frac{1}{3} r^{3} ln (r) - \int \frac{r ^{2}}{3} d r]_{1}^{5}

\int \frac{r ^{2}}{3} d r = \frac{r ^{3}}{9}

= 5 [\frac{1}{3} r^{3} ln (r) - \frac{r ^{3}}{9}]_{1}^{5}

Compute the boundaries:

- \frac{124}{9} + \frac{125}{3} ln (5)

= 5 (- \frac{124}{9} + \frac{125}{3} ln (5))

x \to \infty lim (c^{x})

x \to - \infty lim (2)

y^{^{'}} + y cos (x) = 4 cos (x), y (0) = 6

(- 2.2) (1.2)

\frac{d}{d x} (ln (\frac{x + 8}{x - 8}))

What is the integral from 1 to 5 of 5r^2ln(r) ?
The integral from 1 to 5 of 5r^2ln(r) is 5(-124/9+125/3 ln(5))