What is the integral from 0 to 1 of x^{-1/2}ln(x) ?

The integral from 0 to 1 of x^{-1/2}ln(x) is -4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of x^{-1/2}ln(x)

\int_{0}^{1} x^{- \frac{1}{2}} ln (x) d x

- 4

Solution steps

\int_{0}^{1} x^{- \frac{1}{2}} ln (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

- 4

= - 4

\int_{- \frac{π}{3}}^{\frac{π}{3}} sin (x) d x

\int_{1}^{3} 4 x (x^{2} + 5) d x

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

\int_{2}^{5} \frac{4 - 3 x ^{2}}{x ^{3}} d x

\int_{- 1}^{2} - x^{4} - x^{2} + 6 x + 8 d x

What is the integral from 0 to 1 of x^{-1/2}ln(x) ?
The integral from 0 to 1 of x^{-1/2}ln(x) is -4