What is the integral from 1 to 5 of 4r^2ln(r) ?

The integral from 1 to 5 of 4r^2ln(r) is 4(-124/9+125/3 ln(5))

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integral from 1 to 5 of 4r^2ln(r)

\int_{1}^{5} 4 r^{2} ln (r) d r

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

Decimal

213.12854 \dots

Solution steps

\int_{1}^{5} 4 r^{2} ln (r) d r

Take the constant out:

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

= 4 \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}

= 4 [\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}

= 4 [\frac{1}{3} r^{3} ln (r) - \frac{r ^{3}}{9}]_{1}^{5}

Compute the boundaries:

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

= 4 (- \frac{124}{9} + \frac{125}{3} ln (5))

f (x) = \frac{x}{x ^{2} - x}

\int (x^{3} - 6 x - 9) d x

f (x) = \frac{4 x}{( x - 9 ) ^{5}}

\frac{\partial}{\partial z} (x y e^{x z})

ln (4 x), 1

What is the integral from 1 to 5 of 4r^2ln(r) ?
The integral from 1 to 5 of 4r^2ln(r) is 4(-124/9+125/3 ln(5))