Document and Entity Information	May 03, 2023
Document And Entity Information [Line Items]
Entity Registrant Name	Integral Acquisition Corp 1
Amendment Flag	false
Entity Central Index Key	0001850262
Current Fiscal Year End Date	--12-31
Document Type	8-K
Document Period End Date	May 03, 2023
Entity Incorporation State Country Code	DE
Entity File Number	001-41006
Entity Tax Identification Number	86-2148394
Entity Address, Address Line One	667 Madison Avenue
Entity Address, City or Town	New York
Entity Address, State or Province	NY
Entity Address, Postal Zip Code	10065
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
Units Each Consisting Of One Share Of Class A Common Stock 0.0001 Par Value And One Half Of One Redeemable Warrant [Member]
Document And Entity Information [Line Items]
Security 12b Title	Units, each consisting of one share of Class A common stock, $0.0001 par value, and one-half of one Redeemable Warrant
Trading Symbol	INTEU
Security Exchange Name	NASDAQ
Class A Common Stock 0.0001 Par Value [Member]
Document And Entity Information [Line Items]
Security 12b Title	Class A common stock, $0.0001 par value
Trading Symbol	INTE
Security Exchange Name	NASDAQ
Redeemable Warrants Each Whole Warrant Exercisable For One Class A Common Stock At An Exercise Price Of 11.50 [Member]
Document And Entity 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