v3.25.2
Cover - shares
 6 Months Ended
Jun. 30, 2025
Sep. 19, 2025
Document Type 10-Q  
Amendment Flag false  
Document Quarterly Report true  
Document Transition Report false  
Document Period End Date Jun. 30, 2025  
Document Fiscal Period Focus Q2  
Document Fiscal Year Focus 2025  
Current Fiscal Year End Date --12-31  
Entity File Number 001-41006  
Entity Registrant Name INTEGRAL ACQUISITION CORPORATION 1  
Entity Central Index Key 0001850262  
Entity Tax Identification Number 86-2148394  
Entity Incorporation, State or Country Code DE  
Entity Address, Address Line One 1330 Avenue of the Americas  
Entity Address, Address Line Two 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  
Entity Current Reporting Status Yes  
Entity Interactive Data Current Yes  
Entity Filer Category Non-accelerated Filer  
Entity Small Business true  
Entity Emerging Growth Company true  
Elected Not To Use the Extended Transition Period false  
Entity Shell Company true  
Class A Common Stock [Member]    
Entity Common Stock, Shares Outstanding   3,237,669
Class B Common Stock [Member]    
Entity Common Stock, Shares Outstanding   1