
9.2.1 Integrals depending on a parameter
Problem:
Explore the integral for uniform convergence with respect to the parameter in the region \( E \) :
\[
\begin{array}{l}
\int_{0}^{\infty} \sin (\alpha \sinh x) d x, \\
E=\left[\frac{1}{2}, \infty\right), \quad \sinh x=\frac{e^{x}-e^{-x}}{2} .
\end{array}
\]