By comparing Φ(x) and f(x) we notice Φ(x) contains 3 numerical approximations.
Therefore, we know in advance Φ(x) will take < 3^2 times f(x) + few more
arithmetic operations ... roughly: Φ(x) will take < 100 sec.
Leave the integrator accuracy 100.

Maths Dirac Integral.sm (11 KiB) downloaded 68 time(s).

... [suite], you can replace the two constant terms by their
decimal evaluation. It will drop the timing nearly by ½.
It will not significantly change the the integration due
to the integrator not so accurate !