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

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

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integral of sqrt(ln(x))

\int ln (x) d x

x ln (x) - \frac{π}{2} erfi (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} erfi (ln (x))

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

Add a constant to the solution

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

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