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I am having a lot of trouble trying to solve/analyse this integral:

$$\displaystyle \int_2^\infty \frac{x+y}{(y)(y^2-1)(\ln(x+y))} dy$$

I have tried everything with no result; it seems impossible for me to work with that $\ln(x+y)$.

I have also tried to compute it, but that does not help neither.

It is given that that $x$ will be an integer $x>1$, so it seems obvious that both integrals converge.

What could I do?

Thank you.

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    is $x$ a constant or an independent variable? – 2017-02-05
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    @lam An independent variable. I an trying to get at least the asymptotic behaviour of the integral in terms of $x$ – 2017-02-05
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    It will be helpful to know what conditions are satisfied by ${\large b}$ ?. – 2017-02-05
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    @Felix Corrected – 2017-02-05
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    @user3141592 Since $x$ is a "fixed" value here, you can pick any positive number greater than $1$ for $x$ and then put the function into an online integrator tool. I did wolfram and it couldn't integrate. I am afraid there is no standard anti derivative for your function, no matter what $x$ is – 2017-03-02

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