Why is this the Helmholtz Free Energy for the Onsager Ising Model?

I’m reading through Kerson Huang’s presentation of the Onsager solution. We end up determining that the natural log of the partition function is

$$ln Z = frac{1}{2}ln (frac{2 cosh^2(2 beta epsilon)}{sinh (2 beta epsilon)}) + frac{1}{2 pi}int_0^{pi}dphi ln frac{1}{2}(1+sqrt{1-kappa^2 sin^2 phi})$$

with $epsilon$ and $phi$ being determined from the bond interactions. Now, I understand that the Helmholtz free energy takes the formula $F = -frac{1}{beta} ln Z$. Given this formula, I don’t understand how the book then goes on to say that the Helmholtz free energy is

$$beta F = -ln(2cosh(2 beta epsilon)) – frac{1}{2 pi}int_0^{pi}dphi ln frac{1}{2}(1+sqrt{1-kappa^2 sin^2 phi}).$$

I believe there was a mathematical error made in equating $frac{1}{2}ln (frac{2 cosh^2(2 beta epsilon)}{sinh (2 beta epsilon)})$ and $-ln(2cosh(2 beta epsilon))$ but I’m not entirely sure and am hoping somebody could elucidate what exactly is going on here. Thank you!