Document and Entity Information	Jul. 02, 2024
Document Information [Line Items]
Document Type	8-K
Document Period End Date	Jul. 02, 2024
Entity Registrant Name	Integral Acquisition Corporation 1
Entity Incorporation State Country Code	DE
Entity File Number	001-41006
Entity Tax Identification Number	86-2148394
Entity Address Address Line 1	1330 Avenue of the Americas
Entity Address Address Line 2	23rd Floor
Entity Address City Or Town	New York
Entity Address State Or Province	NY
Entity Address Postal Zip Code	10019
City Area Code	212
Local Phone Number	209-6132
Written Communications	false
Soliciting Material	false
Pre Commencement Tender Offer	false
Pre Commencement Issuer Tender Offer	false
Entity Emerging Growth Company	true
Entity Ex Transition Period	false
Amendment Flag	false
Entity Central Index Key	0001850262
Former Address [Member]
Document Information [Line Items]
Entity Address Address Line 1	667 Madison Avenue
Entity Address City Or Town	New York
Entity Address State Or Province	NY
Entity Address Postal Zip Code	10065
Capital Units [Member]
Document Information [Line Items]
Security 12b Title	Units, each consisting of one share of Class A Common Stock andone-halfof one redeemable Warrant
Trading Symbol	INTEU
Security Exchange Name	NASDAQ
Warrant [Member]
Document Information [Line Items]
Security 12b Title	Redeemable Warrants, each whole warrant exercisable for one Class A Common Stock at an exercise price of $11.50
Trading Symbol	INTEW
Security Exchange Name	NASDAQ
Common Stock [Member]
Document Information [Line Items]
Security 12b Title	Class A common stock, $0.0001 par value
Trading Symbol	INTE
Security Exchange Name	NASDAQ