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Approximate integral for exp(-x)/x

  1. Apr 2, 2013 #1
    I need to evaluate this integral
    [itex]\int_{x_0}^{\infty} \frac{\exp(-x)}{x}\, dx[/itex]
    [itex]x_0 \ll 1[/itex]

    Is there any cute approximate analytical expression? All I get are diverging series all over the place. The function is obviously finite...
  2. jcsd
  3. Apr 2, 2013 #2

    Prudnikov: Integrals and series

    ∫(x,∞) e^(-ax)/x dx = -Ei(-ax) a>0

    Ei(x) = ∫(-∞,x) e^t/t dt is the exponential integral


    Ei(x) = ∫(-∞,x) e^t/dt = C + ln|x| + x + x*x/(2*2!) + ... + x^n/(n*n!) + ...

    C = 0.577215665

    Last edited: Apr 2, 2013
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