Active refers to both quickness and constancy of action; in the former sense it is allied with agile, alert, brisk, etc.; in the latter, with busy, diligent, industrious. The active love employment, the busy are actually employed, the diligent and the industrious are habitually busy.

J. C. Fernald, English Synonyms and Antonyms (1914)

Example sentences

busy This cross street is busy with pedestrian traffic.
diligent Generally, the Japanese are very diligent workers.
persevering Success is always on the side of the persevering.
assiduous He is assiduous in reading as many Russian books as possible.
active Mrs Klein is over 80, but she's still very active.
enterprising He is young and inexperienced, but quite enterprising.

Popularity over time

Word	1850 → 2019	Trend
industrious		falling
busy		rising
diligent		steady
persevering		steady
assiduous		steady
active		steady

Use in printed books, per decade from 1850 to 2019.

By length

4 letters: busy²
5 letters: brisk¹, worky
6 letters: active², hearty², dogged¹
7 letters: dynamic³, notable³, earnest², operose
8 letters: diligent³, tireless³, plodding², studious³, untiring, sedulous
9 letters: energetic⁴, laborious⁴, assiduous³, unwearied, gumptious
10 letters: persistent³
11 letters: painstaking³, persevering⁴
12 letters: enterprising⁴
13 letters: indefatigable⁶

The small number after each word is its number of syllables (busy² = 2 syllables).

In other languages

Français: industrieux
Italiano: industrioso
Español: industrioso