What is the integral from 0 to 2 of (3ln(x))/x ?

The integral from 0 to 2 of (3ln(x))/x is diverges

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of (3ln(x))/x

\int_{0}^{2} \frac{3 ln ( x )}{x} d x

diverges

Solution steps

\int_{0}^{2} \frac{3 ln ( x )}{x} d x

Take the constant out:

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

= 3 \cdot \int_{0}^{2} \frac{ln ( x )}{x} d x

Apply Integration By Parts

: [ln (x) - \int \frac{1 - ln ( x )}{x} d x]_{0}^{2}

= 3 [ln (x) - \int \frac{1 - ln ( x )}{x} d x]_{0}^{2}

\int \frac{1 - ln ( x )}{x} d x = - \frac{( 1 - ln ( x ) ) ^{2}}{2}

= 3 [ln (x) - (- \frac{( 1 - ln ( x ) ) ^{2}}{2})]_{0}^{2}

Simplify

3 [ln (x) - (- \frac{( 1 - ln ( x ) ) ^{2}}{2})]_{0}^{2} : 3 [\frac{1}{2} (ln^{2} (x) + 1)]_{0}^{2}

= 3 [\frac{1}{2} (ln^{2} (x) + 1)]_{0}^{2}

Compute the boundaries:

diverges

= diverges

\frac{d}{d x} (\frac{1}{4} e^{x})

\frac{d}{d x} (ln (\frac{3 + x}{3 - x}))

\int_{0}^{1} (3 e^{x} - 3 x e^{x^{2}}) d x

\int 8 cos (x) d x

x \to π lim (\frac{cos ^{2} ( x )}{x})

What is the integral from 0 to 2 of (3ln(x))/x ?
The integral from 0 to 2 of (3ln(x))/x is diverges