Integral involving exponential functions

[lequan]

Please help give references on solving the following integral:

$$\int\frac{1}{c_{1}e^{ax}+c_{2}e^{bx}}dx$$ where $$a\neq b$$

Thanks a lot in advance.

 

[mathman]

Gradshteyn and Ryzhik is the most complete table of integrals that I am aware of.
They do not have the integral you want, except for special cases, a = - b or a = 0.

 

[lequan]

It seems that we need to get involved in a hypergeometric function, but no more detailed references...

 

[mathman]

It seems that we need to get involved in a hypergeometric function, but no more detailed references...

Are you asking for indefinite integral or definite integral? For definite integral $(0,\infty)$, the reference I cited above has many expressions that look similar to what you have. As I noted above, nothing for indefinite integral.