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

The integral from 1 to 4 of t^2ln(4t) is -7+254/3 ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 1 to 4 of t^2ln(4t)

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

- 7 + \frac{254}{3} ln (2)

Decimal

51.68646 \dots

Solution steps

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

Apply Integration By Parts

= [\frac{1}{3} t^{3} ln (4 t) - \int \frac{t ^{2}}{3} d t]_{1}^{4}

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

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

Compute the boundaries:

- 7 + \frac{254}{3} ln (2)

= - 7 + \frac{254}{3} ln (2)

What is the integral from 1 to 4 of t^2ln(4t) ?
The integral from 1 to 4 of t^2ln(4t) is -7+254/3 ln(2)