What is the integral from 1 to e^8 of ((ln(x))^2)/x ?

The integral from 1 to e^8 of ((ln(x))^2)/x is 512/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to e^8 of ((ln(x))^2)/x

\int_{1}^{e^{8}} \frac{( ln ( x ) ) ^{2}}{x} d x

\frac{512}{3}

Decimal

170.66666 \dots

Solution steps

\int_{1}^{e^{8}} \frac{( ln ( x ) ) ^{2}}{x} d x

Apply u-substitution

: \int_{0}^{8} u^{2} d u

= \int_{0}^{8} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{0}^{8}

= [\frac{u ^{3}}{3}]_{0}^{8}

Compute the boundaries:

\frac{512}{3}

= \frac{512}{3}

\int_{0}^{6} 2 x^{2} d x

\int_{2}^{3} (3 x^{2} - \frac{x ^{4}}{4}) d x

\int_{0}^{1} x sin (1 - x^{2}) d x

\int_{1}^{3} (4 x - 3) d x

\int_{\frac{π}{3}}^{\frac{3 π}{4}} sin (x) d x

What is the integral from 1 to e^8 of ((ln(x))^2)/x ?
The integral from 1 to e^8 of ((ln(x))^2)/x is 512/3