  We study the field-induced quantum phase transitions (QPT) and the relevant
magnetic properties of a spin-1/2 two-leg integrable spin ladder (ISL), of
which the system parameters in bridging to the real compounds are determined by
setting the extra interactions in the Hamiltonian of the ISL relative to the
Heisenberg spin ladder to vanish in the expectation in the ground state (GS).
Such an ISL analytically has the correct leading terms of both the critical
fields of the two QPT's as in the real strongly-coupled compounds: g\mu
_BH_{c1}=J_{\perp}-J_{\parallel} and g\mu_BH_{c2}=J_{\perp}+2J_{\parallel} in
terms of the experimental leg (J_{\parallel}) and rung (J_{\perp})
interactions. The symmetric magnetization inflection point is located at g\mu
_BH_{IP}=J_{\perp}+J_{\parallel}/2. The magnetizations for the GS and at finite
temperatures, as well as the susceptibility, show good agreements in various
comparisons with the finite-site exact diagonalization, the transfer-matrix
renormalization group numerical result, the perturbation theory, and the
compounds (5IAP)_2CuBr_4\cdot 2H_2O, Cu_2(C_5H_{12}N_2)_2Cl_4 and
(C_5H_{12}N)_2CuBr_4.
