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IGR J00291+5934 is the fastest-known accretion-powered X-ray pulsar,discovered during a transient outburst in 2004. In this paper, we report onIntegral and Swift observations during the 2015 outburst, which lasts for$\sim25$ d. The source has not been observed in outburst since 2008, suggestingthat the long-term accretion rate has decreased by a factor of two sincediscovery. The averaged broad-band (0.1 - 250 keV) persistent spectrum in 2015is well described by a thermal Comptonization model with a column density of$N_{\rm H} \approx4\times10^{21}$ cm$^{-2}$, a plasma temperature of $kT_{\rme} \approx50$ keV, and a Thomson optical depth of $\tau_{\rm T}\approx1$.Pulsations at the known spin period of the source are detected in the Integraldata up to the $\sim150$ keV energy band. We also report on the discovery ofthe first thermonuclear burst observed from IGR J00291+5934, which lasts around7 min and occurs at a persistent emission level corresponding to roughly$1.6\%$ of the Eddington accretion rate. The properties of the burst suggest itis powered primarily by helium ignited at a depth of $y_{\rmign}\approx1.5\times10^9$ g cm$^{-2}$ following the exhaustion by steadyburning of the accreted hydrogen. The Swift/BAT data from the first $\sim20$ sof the burst provide indications of a photospheric radius expansion phase.Assuming this is the case, we infer a source distance of $d = 4.2 \pm 0.3$ kpc.

The 2015 outburst of the accretion-powered pulsar IGR J00291+5934: INTEGRAL and Swift observations