The built-in search (as it currently works) is probably not optimal for finding a specific mathematical expression. But still, it can be used sometimes.
For example, I could try to:
Notice that I have used quotation marks to search for a specific expression.
The results are closer - but far from great. The search engine ignores special symbols. And if there is a post about the same integral, but the variable is denoted by $t$ rather than $x$, I won't find it from this search.
There are various search engines which are suitable for mathematical formulas, see the FAQ post: How to search on this site? (This post is mentioned in the help center - it was added based on this feature request: Should we add external searches in some help pages about search?)
For example, at the moment, both ApproachZero and SearchOnMath can be used to find posts on this site. (In ApproachZero you can even search for posts in a specific tag.)
You can use your integral to test them a bit:
And there are certainly various other variation you could try.