What is the integral from 1 to e^7 of ((ln(x))^2)/x ?

The integral from 1 to e^7 of ((ln(x))^2)/x is 343/3

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^7 of ((ln(x))^2)/x

\int_{1}^{e^{7}} \frac{( ln ( x ) ) ^{2}}{x} d x

\frac{343}{3}

Decimal Notation

114.33333 \dots

Solution steps

\int_{1}^{e^{7}} \frac{( ln ( x ) ) ^{2}}{x} d x

Apply u-substitution

: \int_{0}^{7} u^{2} d u

= \int_{0}^{7} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{0}^{7}

= [\frac{u ^{3}}{3}]_{0}^{7}

Compute the boundaries:

\frac{343}{3}

= \frac{343}{3}

\int_{1}^{2} \frac{1}{2 x - x ^{2}} d x

\int_{1}^{4} 1 + (2 x)^{2} d x

\int_{0}^{1} \frac{1}{x e ^{x^{2}}} d x

\int_{0}^{π} \frac{d}{1} (sin (x)) d x

\int_{0}^{4} ln (3 x + 1) d x

What is the integral from 1 to e^7 of ((ln(x))^2)/x ?
The integral from 1 to e^7 of ((ln(x))^2)/x is 343/3