The ornamental design for an integrated bottlegrip, as shown and described.
FIG. 1 is a top perspective view of an integrated bottle grip showing my new design;
FIG. 2 is a bottom perspective view thereof;
FIG. 3 is a front elevation view thereof;
FIG. 4 is a rear elevation view thereof;
FIG. 5 is a top plan view thereof;
FIG. 6 is a bottom plan view thereof;
FIG. 7 is a right elevation view thereof; and,
FIG. 8 is a left elevation view thereof.
The broken lines showing of a bottle body and cap in FIG. 1-8 are included for the purpose of showing environmental structure and form no part of the claimed design.