Document and Entity Information	Nov. 02, 2023
Document And Entity Information [Line Items]
Entity Registrant Name	Integral Acquisition Corp 1
Amendment Flag	true
Entity Central Index Key	0001850262
Current Fiscal Year End Date	--12-31
Document Type	8-K/A
Document Period End Date	Nov. 02, 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
Amendment Description	On November 8, 2023, the Company (as defined below) filed a Current Report on Form 8-K (the “Original Form 8-K”) with the SEC (as defined below). This amendment to the Original Form 8-K (i) corrects for the fact that on December 29, 2021, 50,000 shares of Class B Common Stock (as defined below) were transferred by the Sponsor (as defined below) to an institutional investor (the “Anchor Investor”), and accordingly, the Sponsor at the time of the Original Form 8-K owned 2,825,000 shares of Class B Common Stock as opposed to 2,875,000 shares of Class B Common Stock, and (ii) properly reflects that the Sponsor converted 2,824,999 shares of Class B Common Stock to Class A Common Stock (as defined below) and the Anchor Investor converted 50,000 shares of Class B Common Stock to Class A Common Stock. Except as described above, all other information in the Original Form 8-K remains unchanged.
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 160 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