Integral of 1/cos(x) in CAS

[parisse]

I will investigate, note that
a:=int(1/cos(x)); simplify(a)
returns almost immediatly ln((sin(x)^2+2*sin(x)+1)/(sin(x)^2-2*sin(x)+1))/4
If you are computing an integral with symbolic boundaries that are disjoints, then you should compute the antiderivative and rewrite it at this step then make the difference at the boundaries. This is way more efficient than rewriting the difference of the antiderivatives at the boundaries because you have one less variable and an expression that is twice smaller (there is nothing in simplify that checks for the difference of a same expression at two different points).