What is the integral from 0 to e^2 of ln(x) ?

The integral from 0 to e^2 of ln(x) is e^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to e^2 of ln(x)

\int_{0}^{e^{2}} ln (x) d x

e^{2}

Decimal

7.38905 \dots

Solution steps

\int_{0}^{e^{2}} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{0}^{e^{2}}

= [x ln (x) - \int 1 d x]_{0}^{e^{2}}

\int 1 d x = x

= [x ln (x) - x]_{0}^{e^{2}}

Compute the boundaries:

e^{2}

= e^{2}

\int_{0}^{1} \frac{3}{x ^{2} + 1} d x

\int_{2}^{8} 4 x d x

\int_{0}^{8} 6 t^{2} - 2 t + 5 d t

\int_{- 8}^{8} (x^{\frac{1}{3}}) d x

\int_{0}^{4} (x + 2)^{2} d x

What is the integral from 0 to e^2 of ln(x) ?
The integral from 0 to e^2 of ln(x) is e^2