The discussion revolves around solving the integral \(\int\frac{1}{c_{1}e^{ax}+c_{2}e^{bx}}dx\) where \(a \neq b\). Participants are seeking references and methods for evaluating this integral, considering both indefinite and definite forms.
Participants generally agree on the complexity of the integral and the potential involvement of hypergeometric functions. However, there is no consensus on a specific method or reference for solving the integral.
Limitations include the lack of detailed references for the hypergeometric function approach and the distinction between indefinite and definite integrals, which remains unresolved.
Are you asking for indefinite integral or definite integral? For definite integral [itex](0,\infty)[/itex], the reference I cited above has many expressions that look similar to what you have. As I noted above, nothing for indefinite integral.lequan said:It seems that we need to get involved in a hypergeometric function, but no more detailed references...