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I have the following integral

$\int \limits_{a}^{\infty} \frac{\exp\left(-ax\right)}{\log(x)\left(c+x\right)^2} dx$

that I do not know how to evaluate. Could you please give me a hint?

Thanks in advance.

  • 0
    Let's just say that even without the logarithm the integral is not elementary: $\int \limits_{a}^{\infty} \frac{\exp\left(-ax\right)}{(c+x)^2} dx=\frac{e^{-a^2}}{a+c}+a e^{a c} \text{Ei} (-a(a+c))$ with Ei being the exponential integral. I highly doubt the introduction of the logarithm makes the integral any more simple2016-08-18

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