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

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SUMMARY

The indefinite integral of \( \frac{e^x}{1+x} \) is non-elementary and is expressed as \( \int \frac{e^x}{1+x}dx = \frac{{\rm{Ei}}(x+1)}{e} + C \). This integral is closely related to the exponential integral function, denoted as Ei. Understanding this relationship is crucial for advanced calculus and analysis.

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

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
 

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