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

The integral from e to e^2 of (ln(x^3))/x is 9/2

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^3))/x

\int_{e}^{e^{2}} \frac{ln ( x ^{3} )}{x} d x

\frac{9}{2}

Decimal Notation

4.5

Solution steps

\int_{e}^{e^{2}} \frac{ln ( x ^{3} )}{x} d x

Apply u-substitution

: \int_{e^{3}}^{e^{6}} \frac{ln ( u )}{3 u} d u

= \int_{e^{3}}^{e^{6}} \frac{ln ( u )}{3 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{e^{3}}^{e^{6}} \frac{ln ( u )}{u} d u

Apply u-substitution

: \int_{3}^{6} v d v

= \frac{1}{3} \cdot \int_{3}^{6} v d v

Apply the Power Rule

: [\frac{v ^{2}}{2}]_{3}^{6}

= \frac{1}{3} [\frac{v ^{2}}{2}]_{3}^{6}

Compute the boundaries:

\frac{27}{2}

= \frac{1}{3} \cdot \frac{27}{2}

Simplify

= \frac{9}{2}

\int_{- 2}^{2} \frac{1}{x ^{3}} d x

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

\int_{- 2}^{2} ∣ x - 1 ∣ d x

\int_{1}^{8} \frac{1}{x} d x

\int_{0}^{2} sin (\frac{nπ x}{2}) d x

What is the integral from e to e^2 of (ln(x^3))/x ?
The integral from e to e^2 of (ln(x^3))/x is 9/2