“Is it true that keeping your battery between 40% and 80% makes your battery have a longer lifespan?”

Yes, absolutely, although the usual rule is 80/20.

A li-ion battery is stressed the most during the top and bottom 20% of its charging range; and the closer to 100% or 0% you get, the greater the stress.

In other words, charging from 99% to 100% is way harder on a battery than charging from 49% to 50%, even though both deliver 1% charge.

(You can feel it in the excess heat the battery produces when it’s charged very high or discharged very low).

It’s fine to use the full capacity of your battery when you need it — that’s what it’s there for. But when you can, stop charging at around 80%, more or less, and start recharging at around 20%, more or less, and your battery will age less rapidly, compared to routine full charges.

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