Final answer:
Both integral proteins and transmembrane proteins penetrate the hydrophobic part of the lipid bilayer, with transmembrane proteins being a specific type of integral proteins that span the entire membrane.
Step-by-step explanation:
The kind of membrane protein that penetrates into the hydrophobic part of the lipid bilayer includes integral proteins and transmembrane proteins. Integral proteins are integrated into the membrane structure where their hydrophobic regions interact with the hydrophobic region of the phospholipid bilayer. Whereas, transmembrane proteins span the entire plasma membrane, making them a subset of integral proteins that go across the membrane from one side to the other.
Therefore, the correct answer to which kind of membrane protein penetrates into the hydrophobic part of the lipid bilayer is e) both integral protein and transmembrane protein. Integral proteins may span all or part of the membrane, and some, like transmembrane proteins, extend across the entire membrane touching both the intracellular and extracellular environments.