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

The integral from 1 to 2 of x^2ln(x) is -7/9+8/3 ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 2 of x^2ln(x)

\int_{1}^{2} x^{2} ln (x) d x

- \frac{7}{9} + \frac{8}{3} ln (2)

Decimal Notation

1.07061 \dots

Solution steps

\int_{1}^{2} x^{2} ln (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

- \frac{7}{9} + \frac{8}{3} ln (2)

= - \frac{7}{9} + \frac{8}{3} ln (2)

f (x) = (3 x^{4} + 7)^{6}

\frac{d}{d x} (\frac{2 x ^{3}}{( x ^{2} + 1 ) ^{2}})

\frac{d}{d x} (\frac{2 x y}{1 + x ^{2}})

y^{^{'}} = 2 e^{2 x - y}, y (0) = 0

\frac{d}{d x} (x^{3} - x^{2} + 7 x - 1)

What is the integral from 1 to 2 of x^2ln(x) ?
The integral from 1 to 2 of x^2ln(x) is -7/9+8/3 ln(2)