Hi Vin
If you want numerical value, then try using NIntegrate
In[13]:= Clear[\[Epsilon], h]
In[22]:= h = 0.01; \[Epsilon] = 0.3;
In[23]:= NIntegrate[1.212*((1 - (1 - \[Epsilon]*Cos[(Pi*z)/h])^
(1/2.3))/Cos[(Pi*z)/h]), {z, -h/2, h/2}]
Out[23]= 0.00167881
