Are there any approximations, or expansions to evaluate integrals of the form: $$\int \frac{(x-K)^{-a}}{\log(x)} dt, \quad a \geq 2.$$ Even for a special case of K $\in \mathbb{N}^+$ for example $K = 1, a = 2$, does there exist a closed form expression or even a method to proceed towards an approximation.

  • $\begingroup$ wolframalpha.com/input/… $\endgroup$ – tired Dec 13 '16 at 12:11
  • $\begingroup$ Perhaps look up the logarithmic integral. $\endgroup$ – Simply Beautiful Art Dec 13 '16 at 12:32
  • $\begingroup$ @SimpleArt, I did not get what you meant. Can you please elaborate? $\endgroup$ – Gourab Ghatak Dec 13 '16 at 14:43
  • $\begingroup$ @tired Wolfram Alpha is not giving closed form results. I was wondering if this integral can be approximated by any function. $\endgroup$ – Gourab Ghatak Dec 13 '16 at 14:43
  • $\begingroup$ is one of the parameters big or small? $\endgroup$ – tired Dec 13 '16 at 14:57

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