What is the integral from 0 to 1 of sqrt(-ln(x)) ?

The integral from 0 to 1 of sqrt(-ln(x)) is -Does not exist

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integral from 0 to 1 of sqrt(-ln(x))

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

- Does not exist

Solution steps

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

Compute the indefinite integral:

\int - ln (x) d x = - \frac{π}{2} erf (- ln (x)) + i x ln (x) + C

Compute the boundaries:

\int_{0}^{1} - ln (x) d x = - \frac{π}{2} erf (- ln (1)) + i 1 \cdot ln (1) -

Does not exist

= - \frac{π}{2} erf (- ln (1)) + i 1 \cdot ln (1) - Does not exist

Simplify

= - Does not exist

What is the integral from 0 to 1 of sqrt(-ln(x)) ?
The integral from 0 to 1 of sqrt(-ln(x)) is -Does not exist