What is the integral from e to e^2 of ((ln(x))^4)/x ?

The integral from e to e^2 of ((ln(x))^4)/x is 31/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from e to e^2 of ((ln(x))^4)/x

\int_{e}^{e^{2}} \frac{( ln ( x ) ) ^{4}}{x} d x

\frac{31}{5}

Decimal

6.2

Solution steps

\int_{e}^{e^{2}} \frac{( ln ( x ) ) ^{4}}{x} d x

Apply u-substitution

: \int_{1}^{2} u^{4} d u

= \int_{1}^{2} u^{4} d u

Apply the Power Rule

: [\frac{u ^{5}}{5}]_{1}^{2}

= [\frac{u ^{5}}{5}]_{1}^{2}

Compute the boundaries:

\frac{31}{5}

= \frac{31}{5}

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

\int_{0}^{1} x^{10} ln (x) d x

\int_{1}^{4} 4^{3 x} d x

\int_{x}^{1} ln (t) d t

\int_{0}^{4} π (\frac{12 - 3 x}{4})^{2} d x

What is the integral from e to e^2 of ((ln(x))^4)/x ?
The integral from e to e^2 of ((ln(x))^4)/x is 31/5