How do I solve the integral of 1/ ((e^x)-x)?

Answer 1

Nope.

Needs to be integrated numerically using Simpson's rule, Adapative Quadrature, or Reimann Sums

IN order to do that , you must provide the limits of integration

so the software can approximate the area under the curve.

If you replace e^x with a FINITE series expansion, the x will either cancel or combine

with another term in the polynomial. You can then do a partial fraction decomposition

if it factors, and again, you get just an approximation, and a VERY POOR one at that.