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]
A Laurent series is a representation of a complex function as an infinite sum of powers of the variable, including negative powers.
A Laurent series allows us to express a complex function in a compact and easily manipulatable form, making it easier to perform integrations and other calculations.
The Laurent series for e^x/x can be found by using the Maclaurin series for e^x and then manipulating it to include negative powers of x.
The radius of convergence for the Laurent series of e^x/x is the distance from the center of the series to the nearest singularity, which in this case is x=0. So the radius of convergence is 0.
No, the Laurent series for e^x/x is only valid for values of x within its radius of convergence, which in this case is 0. For other values of x, alternative methods of integration must be used.