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

The integral from 2 to x^2 of ln(t) is 2x^2ln(x)-x^2-2ln(2)+2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

2 x^{2} ln (x) - x^{2} - 2 ln (2) + 2

Solution steps

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

Apply Integration By Parts

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

\int 1 d t = t

= [t ln (t) - t]_{2}^{x^{2}}

Compute the boundaries:

2 x^{2} ln (x) - x^{2} - 2 ln (2) + 2

= 2 x^{2} ln (x) - x^{2} - 2 ln (2) + 2

What is the integral from 2 to x^2 of ln(t) ?
The integral from 2 to x^2 of ln(t) is 2x^2ln(x)-x^2-2ln(2)+2