Rmpfr::integrateR with the quadpack qagi method to handle
integration involving infinity. Qagi is a transformation of $x/sigma=(1-t)/t$ for positive x,
and $x/sigma=(t-1)/t$ for negative x. $t=0$ is represented by .Machine$double.eps.
This utility requires (a) lower or upper is +/-Inf;
(b) lower and upper are of the same sign.
ecd.mpfr_qagi(object, f, lower, upper, ..., abs.tol = .Machine$double.eps^0.25, show.warning = TRUE)f.integrate object