What is the integral from 1 to 4 of sqrt(ln(x)) ?

The integral from 1 to 4 of sqrt(ln(x)) is 4sqrt(2)sqrt(ln(2))-(sqrt(pi))/2 \erfi(sqrt(ln(4)))

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integral from 1 to 4 of sqrt(ln(x))

\int_{1}^{4} ln (x) d x

42 ln (2) - \frac{π}{2} erfi (ln (4))

Solution steps

\int_{1}^{4} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int \frac{1}{2 ln ( x )} d x]_{1}^{4}

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

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

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

Compute the boundaries:

42 ln (2) - \frac{π}{2} erfi (ln (4))

= 42 ln (2) - \frac{π}{2} erfi (ln (4))

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What is the integral from 1 to 4 of sqrt(ln(x)) ?
The integral from 1 to 4 of sqrt(ln(x)) is 4sqrt(2)sqrt(ln(2))-(sqrt(pi))/2 \erfi(sqrt(ln(4)))