What is the integral from 1 to 3 of 7r^3ln(r) ?

The integral from 1 to 3 of 7r^3ln(r) is 7(-5+81/4 ln(3))

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integral from 1 to 3 of 7r^3ln(r)

\int_{1}^{3} 7 r^{3} ln (r) d r

7 (- 5 + \frac{81}{4} ln (3))

Decimal Notation

120.72829 \dots

Solution steps

\int_{1}^{3} 7 r^{3} ln (r) d r

Take the constant out:

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

= 7 \cdot \int_{1}^{3} r^{3} ln (r) d r

Apply Integration By Parts

: [\frac{1}{4} r^{4} ln (r) - \int \frac{r ^{3}}{4} d r]_{1}^{3}

= 7 [\frac{1}{4} r^{4} ln (r) - \int \frac{r ^{3}}{4} d r]_{1}^{3}

\int \frac{r ^{3}}{4} d r = \frac{r ^{4}}{16}

= 7 [\frac{1}{4} r^{4} ln (r) - \frac{r ^{4}}{16}]_{1}^{3}

Compute the boundaries:

- 5 + \frac{81}{4} ln (3)

= 7 (- 5 + \frac{81}{4} ln (3))

\frac{4}{2 ( s - 3 ) ^{2} - 50}

f (x) = (x^{3} - 4 x + 1) e^{x}, at x = 0

x^{2} + 2 x + 2, 2 x^{2} + 3 x - 4

\frac{d}{d x} (ln (x^{2} + 7))

x \to \frac{π}{2} lim (sin (x))

What is the integral from 1 to 3 of 7r^3ln(r) ?
The integral from 1 to 3 of 7r^3ln(r) is 7(-5+81/4 ln(3))