Recent studies of the optical properties of semiconducting single-walled carbon nanotubes suggest that these truly nanometre-scale systems have a promising future in nanophotonics, in addition to their well-known potential in electronics. Semiconducting single-walled nanotubes have a direct, diameter-dependent bandgap and can be excited readily by current injection, which makes them attractive as nano-emitters. The electroluminescence is spectrally broad, spatially non-directional, and the radiative yield is low. Here we report the monolithic integration of a single, electrically excited, semiconducting nanotube transistor with a planar lambda/2 microcavity, thus taking an important first step in the development of nanotube-based nanophotonic devices. The spectral full-width at half-maximum of the emission is reduced from approximately 300 to approximately 40 nm at a cavity resonance of 1.75 microm, and the emission becomes highly directional. The maximum enhancement of the radiative rate is estimated to be 4. We also show that both the optically and electrically excited luminescence of single-walled nanotubes involve the same E11 excitonic transition.