I need to estimate the area between the functions 

$f(x) = \log(x+1)/x \, , f(x-1), \, y=0$, and $y=a$. where $a>1$. 
Now I have tried quite a few ways to do this, but nothing comes to mind.

I tried writing out the taylor series, I tried changing this around. 
Nothing really gave a decent approximation. 

A decent in my mind would be anything greater than one decimal. Eg an error less than $E<10^2$.

Cheers =)

EDIT: After making a nice drawing it seems that if $a>>0$ then $A \approx a + \frac{1}{12}\pi^2$

![Image](https://i.stack.imgur.com/iSK8U.png)