1-ln-x-dx-

Question Number 132110 by Raxreedoroid last updated on 11/Feb/21

\int \frac{1}{\ln x} d x = ?

Answered by Olaf last updated on 11/Feb/21

F (x) = \int \frac{d x}{\ln x}

Let x = e^{u}

F (e^{u}) = \int \frac{d (e^{u})}{\ln (e^{u})} = \int \frac{e^{u}}{u} d u = Ei (u)

u = \ln x

F (x) = Ei (\ln x) (+ C)

Commented by Raxreedoroid last updated on 11/Feb/21

What is Ei ?

Commented by Olaf last updated on 11/Feb/21

Ei (x) = \int_{- \infty}^{x} \frac{e^{t}}{t} d t

(integral exponential function)

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