Question 1027574
{{{f(x) = ln(1+x^2)}}} approaches +{{{infinity}}} as x goes to +{{{infinity}}}.  (Obvious!)

{{{df/dx = (2x)/(1+x^2)}}} goes to 0 as x goes to +{{{infinity}}}. (The first derivative is also positive starting at x = 0, hence the graph is increasing as x goes to infinity.)

{{{d^2f/dx^2 = (2-2x^2)/(1+x^2)^2}}} goes to 0 as x goes to +{{{infinity}}}. (The second derivative is negative for x > 0 hence the graph is concave downward there.)

The preceding information suggest that ln(1+x^2) increases, but slows down significantly as x goes to infinity.  (Similar to a 'diminishing returns" behavior.)