Why doesn't Mathematica evaluate the well-known Ahmed integral? $$ \int_0^1 \frac{\tan ^{-1}\left(\sqrt{x^2+2}\right)}{\left(x^2+1\right) \sqrt{x^2+2}} \, dx $$
Mathematica did it this way:
Looking at https://mathworld.wolfram.com/AhmedsIntegral.html it seems that Mathematica evaluates the generic integrals but not to the same results from the article.
I will venture the obvious reason, that it does not know how to do this integral.
