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Context. The H3O+ molecule probes the chemistry and the ionization rate of dense circumnuclear gas in galaxies. Aims. We use the H3O+ molecule to investigate the impact of starburst and AGN activity on the chemistry of the molecular interstellar medium. Methods. Using the JCMT, we have observed the 32+ – 22+ 364 GHz line of p-H3O+ towards the centres of seven active galaxies. Results. We have detected p-H3O+ towards IC 342, NGC 253, NGC 1068, NGC 4418, and NGC 6240. Upper limits were obtained for IRAS 15250 and Arp 299. We find large H3O+ abundances (N(H3O+)/N(H2) ≳ 10-8) in all detected galaxies apart from in IC 342 where it is about one order of magnitude lower. We note, however, that uncertainties in N(H3O+) may be significant due to lack of definite information on source size and excitation. We furthermore compare the derived N(H3O+) with N(HCO+) and find that the H3O+ to HCO+ column density ratio is large in NGC 1068 (24), moderate in NGC 4418 and NGC 253 (4–5), slightly less than unity in NGC 6240 (0.7) and lowest in IC 342 (0.2–0.6). We compare our results with models of X-ray and photon dominated regions (XDRs and PDRs). Conclusions. For IC 342 we find that a starburst PDR chemistry can explain the observed H3O+ abundance. For the other galaxies, the large H3O+ columns are generally consistent with XDR models. In particular for NGC 1068 the elevated N(H3O+)/N(HCO+) ratio suggests a low column density XDR. For NGC 4418 however, large HC3N abundances are inconsistent with the XDR interpretation. An alternative possibility is that H3O+ forms through H2O evaporating off dust grains and reacting with HCO+ in warm, dense gas. This scenario could also potentially fit the results for NGC 253. Further studies of the excitation and distribution of H3O+ – as well as Herschel observations of water abundances – will help to further constrain the models