TimedIntegrate[exp, vars] is like
Integrate, but stops after the number of seconds specified
by the option Timing. Options of Integrate can
be given and are passed on.
This should reach to be done
TimedIntegrate[Log[x^5], {x, 0, 1}, Timing -> 1]-5
This shouldn’t
TimedIntegrate[Log[Cos[x^5]], {x, 0, 1}, Timing -> 10, Integrate -> int]\text{int}\left(\log \left(\cos \left(x^5\right)\right),\{x,0,1\},\text{Assumptions}\to \varepsilon >0\right)