What is the integral of 1/(ln(u)) ?

The integral of 1/(ln(u)) is \Ei(ln(u))+C

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integral of 1/(ln(u))

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

Ei (ln (u)) + C

Solution steps

\int \frac{1}{ln ( 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

v = ln (u)

= Ei (ln (u))

Add a constant to the solution

= Ei (ln (u)) + C