What is the integral from 0 to 1 of (ln(x))/(x^{1/3)} ?

The integral from 0 to 1 of (ln(x))/(x^{1/3)} is -9/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 1 of (ln(x))/(x^{1/3)}

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

- \frac{9}{4}

Decimal

- 2.25

Solution steps

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

Apply Integration By Parts

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

\int \frac{3}{2 x ^{\frac{1}{3}}} d x = \frac{9}{4} x^{\frac{2}{3}}

= [\frac{3}{2} x^{\frac{2}{3}} ln (x) - \frac{9}{4} x^{\frac{2}{3}}]_{0}^{1}

Compute the boundaries:

- \frac{9}{4}

= - \frac{9}{4}

What is the integral from 0 to 1 of (ln(x))/(x^{1/3)} ?
The integral from 0 to 1 of (ln(x))/(x^{1/3)} is -9/4