(\[Integrated\]) by means of Eq. (\[tau\]), we obtain $$\label{Integrated-1}
\frac{R^2 - 4 R_c^2}{2} + (R_\sigma + R_c)(R_\sigma - 2 R_c) + (R_\sigma + R_c) R_c \ln\left(\frac{R}{R_c} - 1\right) = D s \zeta t\; .$$

Validity of the general relation Eq. (\[Integrated-1\]), which strictly takes into account Laplace pressure influence on the bubble growth process, is limited only by the condition of applicability of steady approximation Eq. (\[Flux\]) for the diffusion flux. Equation (\[Integrated-1\]) does not imply the smallness of quantity $R_c/R_\sigma$ which follows from Eqs. (\[R\_s-R\_c-Henry\]) and (\[Strong-Zeta-Henry\]). Eq. (\[Integrated-1\]) complies with the results obtained in papers \[\[Epstein-Plesset\], \[Cable-Frade\]\] for the particular case of steady growth of a bubble.

Now let us consider the third stage of bubble growth, when $R \geq R_\sigma$. First of all, let us note that at the end of the first stage, when the bubble radius $R$ approaches the value $(R_cR_\sigma)^{1/2}$, and with even more assurance on the second and the third stages, one can neglect the logarithmic addend in Eq. (\[Integrated-1\]). Moreover, since during the third stage the main contribution in the l. h. s. of Eq. (\[Integrated-1\]) gradually tends to the first addend, equal to $R^2/2$; and the contribution of the second addend 