On the inside; within.
[Latin intra, inside.]
This form is widely used in scientific fields, especially biology and medicine: intracellular, located within a cell or cells; intramolecular, existing or taking place within a molecule; intramuscular, situated or taking place within, or administered into, a muscle; intrauterine, within the uterus; intravenous, existing or taking place within, or administered into, a vein or veins. Other examples are intramural, situated or done within the walls of a building, or one institution; intrapreneur, a manager within a company who promotes innovative product development and marketing (from entrepreneur). The opposite is extra-.
However, intransigent contains Latin in-, not, plus transigere, come to an understanding; intractable similarly derives from Latin tractabilis, from tractare, to handle.