MHB What Is the Indefinite Integral of \( \frac{e^x}{1+x} \)?

[juantheron]

$\displaystyle \int \frac{e^x}{1+x}dx$

 

[CaptainBlack]

$\displaystyle \int \frac{e^x}{1+x}dx$

This is non-elementary and closely related to the exponential integral.

$\displaystyle \int \frac{e^x}{1+x}dx=\frac{{\rm{Ei}}(x+1)}{e}+C$

CB