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

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

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

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

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

Decimal Notation

106.56427 \dots

Solution steps

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

Take the constant out:

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

= 2 \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}

= 2 [\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}

= 2 [\frac{1}{3} r^{3} ln (r) - \frac{r ^{3}}{9}]_{1}^{5}

Compute the boundaries:

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

= 2 (- \frac{124}{9} + \frac{125}{3} ln (5))

\frac{d}{d x} (ln (x^{2} + 4 x))

y = x, y = 2 - x, y = 0

y = 2 sin (x), y = e^{x}, x = 0, x = \frac{π}{2}

y^{^{'}} = x^{2} - 3 y

\int (e^{- x}) d x

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