The internal energy per molecule for a diatomic (non-rigid) gas is...

For a non-rigid diatomic gas, the molecules possess translational, rotational, and vibrational motion.

The degrees of freedom are distributed as follows:
Translational degrees of freedom = $3$
Rotational degrees of freedom = $2$
Vibrational degrees of freedom = $2$ (one for kinetic energy and one for potential energy)

Total degrees of freedom $f = 3 + 2 + 2 = 7$

According to the law of equipartition of energy, the average energy associated with each degree of freedom per molecule is $\dfrac{1}{2}k_B T$.

Internal energy per molecule = $\dfrac{f}{2} k_B T = \dfrac{7}{2} k_B T$

Answer: $\dfrac{7}{2}k_B T$