What is the integral of 1/(sqrt(x)ln(x)) ?

The integral of 1/(sqrt(x)ln(x)) is \Ei((ln(x))/2)+C

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integral of 1/(sqrt(x)ln(x))

\int \frac{1}{x ln ( x )} d x

Ei (\frac{ln ( x )}{2}) + C

Solution steps

\int \frac{1}{x ln ( x )} d x

Apply u-substitution

= \int \frac{e ^{\frac{u}{2}}}{u} d u

Apply u-substitution

= \int \frac{e ^{v}}{v} d v

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= Ei (v)

Substitute back

= Ei (\frac{ln ( x )}{2})

Add a constant to the solution

= Ei (\frac{ln ( x )}{2}) + C

What is the integral of 1/(sqrt(x)ln(x)) ?
The integral of 1/(sqrt(x)ln(x)) is \Ei((ln(x))/2)+C