What is the integral from 0 to 1 of x^{-0.5}ln(x) ?

The integral from 0 to 1 of x^{-0.5}ln(x) is -4

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integral from 0 to 1 of x^{-0.5}ln(x)

\int_{0}^{1} x^{- 0.5} ln (x) d x

- 4

Solution steps

\int_{0}^{1} x^{- 0.5} ln (x) d x

Simplify

x^{- 0.5} ln (x) : \frac{ln ( x )}{x}

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

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

- 4

= - 4

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What is the integral from 0 to 1 of x^{-0.5}ln(x) ?
The integral from 0 to 1 of x^{-0.5}ln(x) is -4