A 68-year-old male with COPD is admitted to ICU with acute hypercapnic respiratory failure (pH 7.25, PaCO₂ 65 mmHg, PaO₂ 55 mmHg on O₂). He is initiated on non-invasive ventilation but deteriorates over 6 hours. Intubation is planned. Which investigation is most appropriate to confirm correct endotracheal tube placement and assess ventilation adequacy immediately after intubation?