A nuclear reactor includes a nuclear reactor core comprising fissile material disposed in a reactor pressure vessel having vessel penetrations that exclusively carry flow into the nuclear reactor and at least one vessel penetration that carries flow out of the nuclear reactor. An integral isolation valve (IIV) system includes passive IIVs each comprising a check valve built into a forged flange and not including an actuator, and one or more active IIVs each comprising an active valve built into a forged flange and including an actuator. Each vessel penetration exclusively carrying flow into the nuclear reactor is protected by a passive IIV whose forged flange is directly connected to the vessel penetration. Each vessel penetration carrying flow out of the nuclear reactor is protected by an active IIV whose forged flange is directly connected to the vessel penetration. Each active valve may be a normally closed valve.