Cover Page - USD ($)	12 Months Ended
	Dec. 31, 2023	Apr. 11, 2024	Jun. 30, 2023
Document Information [Line Items]
Document Type	10-K
Amendment Flag	false
Document Fiscal Year Focus	2023
Document Fiscal Period Focus	FY
Document Annual Report	true
Document Transition Report	false
Current Fiscal Year End Date	--12-31
Document Period End Date	Dec. 31, 2023
Entity File Number	001-41006
Entity Registrant Name	INTEGRAL ACQUISITION CORPORATION 1
Entity Central Index Key	0001850262
Entity Incorporation, State or Country Code	DE
Entity Tax Identification Number	86-2148394
Entity Address, Postal Zip Code	10065
City Area Code	212
Local Phone Number	209-6132
Entity Filer Category	Non-accelerated Filer
Entity Small Business	true
Entity Emerging Growth Company	true
Entity Shell Company	true
Entity Address, Address Line One	667 Madison Avenue
Entity Address, City or Town	New York
Entity Address, State or Province	NY
Entity Current Reporting Status	Yes
Entity Interactive Data Current	Yes
Entity Ex Transition Period	false
Entity Well-known Seasoned Issuer	No
Entity Voluntary Filers	No
ICFR Auditor Attestation Flag	false
Entity Public Float			$ 31,814,380.5
Auditor Name	Marcum LLP
Auditor Firm ID	688
Auditor Location	Houston, Texas
Document Financial Statement Error Correction [Flag]	false
Common Stock [Member]
Document Information [Line Items]
Security Exchange Name	NASDAQ
Title of 12(b) Security	Class A Common Stock, par value $0.0001 per share
Trading Symbol	INTE
Capital Units [Member]
Document Information [Line Items]
Security Exchange Name	NASDAQ
Title of 12(b) Security	Units, each consisting of one share of Class A Common Stock and one-half of one redeemable Warrant
Trading Symbol	INTEU
Warrant [Member]
Document Information [Line Items]
Security Exchange Name	NASDAQ
Title of 12(b) Security	Warrants, each exercisable for one shares ofClass A Common Stock for $11.50 per share
Trading Symbol	INTEW
Common Class A [Member]
Document Information [Line Items]
Entity Common Stock, Shares Outstanding		4,073,341
Common Class B [Member]
Document Information [Line Items]
Entity Common Stock, Shares Outstanding		1