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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Decimal Notation

17.24689 \dots

Solution steps

\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}

= [\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}

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

Compute the boundaries:

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

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

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

7 x^{2} - x^{3}

(x - 2) (4 x + 2)

4^{s i n^{2} (x) + c o s (3 x)}

(\frac{1}{t})^{^{'}}

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