What is the integral of sqrt(-ln(x)) ?

The integral of sqrt(-ln(x)) is -(sqrt(pi))/2 \erf(sqrt(-ln(x)))+ixsqrt(ln(x))+C

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integral of sqrt(-ln(x))

\int - ln (x) d x

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

Solution steps

\int - ln (x) d x

Apply Integration By Parts

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

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

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

= x - ln (x) - \frac{π}{2} erf (- ln (x))

Simplify

x - ln (x) - \frac{π}{2} erf (- ln (x)) : - \frac{π}{2} erf (- ln (x)) + i x ln (x)

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

Add a constant to the solution

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

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What is the integral of sqrt(-ln(x)) ?
The integral of sqrt(-ln(x)) is -(sqrt(pi))/2 \erf(sqrt(-ln(x)))+ixsqrt(ln(x))+C