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

The integral from 1 to e of ((ln(t))^2)/t is 1/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 1 to e of ((ln(t))^2)/t

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

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

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

Apply u-substitution

= \int_{0}^{1} u^{2} d u

Apply the Power Rule

= [\frac{u ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= \frac{1}{3}

What is the integral from 1 to e of ((ln(t))^2)/t ?
The integral from 1 to e of ((ln(t))^2)/t is 1/3