7
$\begingroup$

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.

  • 3
    Is the denominator $(c+x)^2\log x$ or $\log[x(c+x)^2]$?2012-07-27
  • 2
    @Mercy: The TeX code (right-clicking the equation) gives the denominator as "\log{x}(c+x)^2". Although verification from OP would be nice...2012-08-15
  • 0
    The integral diverges for $a\le1$.2015-04-10
  • 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

0 Answers 0