Speaker-normalization and -adaptation methods are essential components of state-of-the-art speech recognition systems nowadays. Recently, so-called invariant integration features were presented which are motivated by the theory of invariants. While it was shown that the integration features outperform MFCCs when used with a basic monophone recognition system, it was left open, if their benefits still can be observed when a more sophisticated recognition system with speaker-normalization and/or speaker-adaptation components is used. This work investigates the combination of the integration features with standard speaker-normalization and -adaptation methods. We show that the integration features benefit from adaptation methods and significantly outperform MFCCs in matching, as well as in mismatching training-test conditions.