9.2.30 Integrals depending on a parameter

Problem: Investigate the uniform convergence of the integral on the set \( Y \). \[ \int_{0}^{1} \frac{x^{2} \alpha-\alpha^{3}}{\sqrt{x}\left(\alpha^{2}+x^{2}\right)^{2}} d x, \quad Y=(0 ; 1) . \]