# Integrals of power-logarithm combonations

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.

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