Divergence of $\int\limits_{-\infty}^{+\infty}\frac{1}{\ln(x^2+1)}\textrm{d}x$ [closed]

I was looking for a function $f$ which verifies (I do not know if it exists) :

1. $f:\mathbb{R}\rightarrow\mathbb{R}$
2. $\forall x\in\mathbb{R},\;f(x)\geq 0$
3. $\lim\limits_{x\rightarrow-\infty}f(x)=\lim\limits_{x\rightarrow+\infty}f(x)=0$
4. $\int\limits_{-\infty}^{+\infty}f(x)\textrm{d}x=+\infty$

Here is a candidate I tried, but I cannot prove it diverges :

$$\int\limits_{-\infty}^{+\infty}\frac{1}{\ln(x^2+1)}\textrm{d}x$$