Integration of Ei function

Questions
1

Hi,
I want to integrate the function Exp[A*x]/(B-x) for x, within the limits 0 to N. What I could figure out by now is that I have to use ExpIntegralEi function for such kind of integrations in mathematica, but not able to get the complete solution. Please let me know how could I get my integration done.

thanks
SHG

2

It works for me on version 9.0.1

Integrate[Exp[a*x]/(b - x), {x, 0, n}]

ConditionalExpression[
 E^(a b) (-Gamma[0, a b] + Gamma[0, a (b - n)] + Log[b] - Log[a b] - 
    Log[b - n] + Log[a (b - n)]),  Im[b/n] != 0 || Re[b/n] > 1 || Re[b/n] < 0]

Could you show what you actually typed? It is better to use lower case letters. Also “N” is reserved symbol in Mathematica.

3

The standered form of Ei function is, Ei(z) = -Integrate[Exp[-t]/t, {t, -z, infinite]. But for the function I am trying to integrate, this needs to be modified..