The integral of the function \(\int \frac{e^x}{x}dx\) is expressed as the exponential integral function, \(\text{Ei}(x)\). While one participant suggested using a Laurent series for term-by-term integration, they also noted the limitations of integration by parts due to the increasing complexity of the expression. The discussion highlights that traditional methods may not yield a straightforward solution, and references to Abramowitz & Stegun's book provide a valuable resource for series expansion techniques related to this integral.
PREREQUISITESMathematicians, students studying calculus, and anyone interested in advanced integration techniques and series expansions.
This just keeps expanding. Using ILATE, the algebraic part should be u, but this just keeping increasing in the power on the bottom. I don't think it's a good candidate for parts.courtrigrad said:why can't you just use integration by parts twice? [tex]\int e^{x}\frac{1}{x} dx[/tex], [tex]u = e^{x}, du = e^{x}dx, dv = \frac{1}{x}, v = \ln x[/tex]