I don't want an easy answer to this problem. However, I would be happy if you could provide me with theorems and/or techniques required to solve it.

$\displaystyle $\lim _{x\to \infty }x^2(ln({x+1\over x}) +ln({2x+3\over 2x}))$$

I know that $\displaystyle $\lim _{x\to \infty }({x+1\over x}) = \lim _{x\to \infty }(1+{1\over x})^1 = e $$ But the natural logarithm is in the way and I think that you can't calculate the limit IN the logarithm first.

Thanks in advance

P.S. Oh, and by the way could anyone recommend a book on calculus with challenging problems, because most of the usual calculus textbooks aren't rigorous enough for my college course. (My lecturer always finds a way to give much more complicated problems than those in textbooks)