This minimal example
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
A
&\leq
\begin{aligned}[t]
&\int \text{first part of a long expression}
\\& \times \text{second part of the long expression}
\end{aligned}
\\&\leq \int \text{shorther expression}
\end{align*}
\end{document}
gives
The two integral signs are not aligned because there is too much space before the first ones (or equivalently, before the aligned environment).
How can I get the correct horizontal space before the first integral sign?
\! \begin{aligned}....
this removes the added space in front ofaligned
\!
solved the problem.