Primitive of Exponential Integral Function

Theorem

 * $\displaystyle \int \map \Ei x \rd x = x \map \Ei x - e^{-x} + C$

where:
 * $\Ei$ denotes the exponential integral function
 * $x$ is a strictly positive real number.

Proof
By Derivative of Exponential Integral Function, we have:


 * $\displaystyle \frac \d {\d x} \paren {\map \Ei x} = -\frac {e^{-x} } x$

So: