What is the integral from 1 to e of (((ln(x))^5))/x ?

The integral from 1 to e of (((ln(x))^5))/x is 1/6

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 of (((ln(x))^5))/x

\int_{1}^{e} \frac{( ( ln ( x ) ) ^{5} )}{x} d x

\frac{1}{6}

Decimal Notation

0.16666 \dots

Solution steps

\int_{1}^{e} \frac{( ln ( x ) ) ^{5}}{x} d x

Apply u-substitution

: \int_{0}^{1} u^{5} d u

= \int_{0}^{1} u^{5} d u

Apply the Power Rule

: [\frac{u ^{6}}{6}]_{0}^{1}

= [\frac{u ^{6}}{6}]_{0}^{1}

Compute the boundaries:

\frac{1}{6}

= \frac{1}{6}

\int_{2 y}^{3 - y} (x + y) d x

\int_{1}^{5} (3 + \frac{2}{x}) d x

\int_{0}^{2} r^{3} 4 - r^{2} d r

\int_{1}^{3} (2 x^{2} - 1) d x

\int_{- 7}^{0} 5 + 49 - x^{2} d x

What is the integral from 1 to e of (((ln(x))^5))/x ?
The integral from 1 to e of (((ln(x))^5))/x is 1/6