What is the integral from 2 to 6 of t^2ln(2t) ?

The integral from 2 to 6 of t^2ln(2t) is 72ln(12)-208/9-16/3 ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 6 of t^2ln(2t)

\int_{2}^{6} t^{2} ln (2 t) d t

72 ln (12) - \frac{208}{9} - \frac{16}{3} ln (2)

Decimal Notation

152.10538 \dots

Solution steps

\int_{2}^{6} t^{2} ln (2 t) d t

Apply Integration By Parts

: [\frac{1}{3} t^{3} ln (2 t) - \int \frac{t ^{2}}{3} d t]_{2}^{6}

= [\frac{1}{3} t^{3} ln (2 t) - \int \frac{t ^{2}}{3} d t]_{2}^{6}

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

= [\frac{1}{3} t^{3} ln (2 t) - \frac{t ^{3}}{9}]_{2}^{6}

Compute the boundaries:

72 ln (12) - \frac{208}{9} - \frac{16}{3} ln (2)

= 72 ln (12) - \frac{208}{9} - \frac{16}{3} ln (2)

y = \frac{7 x}{x - 3}, (6, 14)

(x)^{2}

\frac{\partial}{\partial y} (y + x)

y = \frac{1}{( 9 x ^{3} )}, 1, 100

What is the integral from 2 to 6 of t^2ln(2t) ?
The integral from 2 to 6 of t^2ln(2t) is 72ln(12)-208/9-16/3 ln(2)