We demonstrate a quantitative X-ray phase contrast imaging (XPCI) technique derived from propagation dependent phase change. We assume that the absorption and phase components are correlated and solve the Transport of Intensity Equation (TIE). The experimental setup is simple compared to other XPCI techniques; the only requirements are a micro-focus X-ray source with sufficient temporal coherence and an X-ray detector of sufficient spatial resolution. This method was demonstrated in three scenarios, the first of which entails identification of an index-matched sphere. A rubber and nylon sphere were immersed in water and imaged. While the rubber sphere could be plainly seen on a radiograph, the nylon sphere was only visible in the phase reconstruction. Next, the technique was applied to differentiating liquid samples. In this scenario, three liquid samples (acetone, water, and hydrogen peroxide) were analyzed using both conventional computed tomography (CT) and phase contrast CT. While conventional CT was capable of differentiating between acetone and the other two liquids, it failed to distinguish between water and hydrogen peroxide; only phase CT was capable of differentiating all three samples. Finally, the technique was applied to CT imaging of a human artery specimen with extensive atherosclerotic plaque. This scenario demonstrated the increased sensitivity to soft tissue compared to conventional CT; it also uncovered some drawbacks of the method, which will be the target of future work. In all cases, the signal-to-noise ratio of phase contrast was greatly enhanced relative to conventional attenuation-based imaging.