My little experience with a few subs and a microphone setup suggests me that a bass equalizer with Q factor, frequency and amplitude adjustment for a few frequencies is mandatory for a proper equalization in my room. And yes, a measuring system is also needed.
But I never managed to fully integrate a small speaker with a sub - as some people say the best speakers to use with a sub is one that does not need it. The best sub integration i have ever listened to used the Martin Logan Descent sub with Martin Logan Prodigy's.
microstrip
No problem with the first part of your reply but do take a seocnd and reread your post.
a bass equalizer with Q factor, frequency and amplitude adjustment for a few frequencies is mandatory for a proper equalization in my room
How would you accomplish this with a full range speaker? Are you suggesting to place an equalizer in the main signal chain? i doubt that is what you meant but ...
The reality of the situation is when facts clashes with belief or to be more precise belief
systems because there is an audiophile core of beliefs, a system if you will. The physical fact is that the best position for imaging, soundstage and the rest of the spectrum is usually not the best for optimal bass reproduction. This is dues to physics and no amount of wishful thinking will change that. Thus we find the best compromise in separating the subs from the mains. There again audiophile orthodoxy wants the subs, preferably towers to be in close proximity to the mains... Often not their best positions for optimum bass. For the most part in most rooms virtually all speakers regardless of bass capability,
need subwoofers, preferably more than 2 but definitely not one.
It should be noted that in the bass harmonics are often more audible than the fundamental. While 30 Hz is mostly a rumble its first harmonics 60 Hz can be perceived as low bass by most and is very audible. The third harmonics is squat in the region of high ear sensitivity 90 Hz and the fourth is 120 Hz .. you are getting the drift, thus for clean bass reproduction one needs a driver/amplifier with low distortion and power to control the cone (most likely candidate for true low bass unless you go rotary subs but then 20Hz is your upper limit

). You need the appropriate power to control the driver to maximum extension without the amp suffering and sending garbage to the driver. You want a strong and accurate amp. The notion of using similar amps will sound good to us audiophiles and we will find ourselves using extremely powerful
tubes amplifiers on subs or woofer towers to “match" the mains. Not the best combo if you ask me and a waste of quality watts .. but the system will look impressive, cost a lot and sound reasonably good.. Although a Class D amp would have been a better match. Often when subs are used in a system, sight helping, many will claim a lack of integration and a bass “flavor” different from the mains sound. Often an honest assessment and an open mind would tell a different story. Anyone who has heard Steve Williams’ system can attest to that, the bass is integrated with the main despite the abyss of difference between the amps in the JL Audio SS likely Class D or AB, very high power with DSP for sure and the Direct Heated Triode SET he uses for the mains and I have had the same experience having lived very closely for over two years with Genesis speakers (the II and the V) which use their own bass amplifiers. The bass would take the "flavor "of the main amplifiers in all cases. You could even judge of the quality of the main amplifier bass performance through the Genesis although they have their own amp. Such is the case with a good subwoofer set-up. Steve Williams system uses subwoofer and the last time I heard it, was with the JL Audio Gotham (@Steve, I still regret you selling these by the way, they would have worked great in this room) there wasn’t a lack of integration to my ears, to Steve’s and most who have heard his system. I am speaking for myself here: the Magnepan integrated very with Paradigm subwoofers, I know someone on this board who uses MG 3.7 with cone subs. Additionally, many here use speakers with integrated subs and I have NO doubt their bass is well integrated. Jack D201, mep, Mike Lavigne, etc. come to mind.
Long post but to repeat my answer to the original question. Use a good powerful amp , it is good also to add a flexible crossover/Equalizer with your subs, Digital is good for the purpose the best commercial subs use digital EQ with great results ( paradigm Sub-1, JL Audio Gotham, etc) …