\input amstex
\input cyracc.def
\font\tencyr=wncyr10
\def\cyr#1{{\tencyr\cyracc#1}}

\cyr{Dat je integral }
$$I(\alpha)=\int_0^1\frac{\ln(1-\alpha^2x^2)}
{x\,\sqrt{1-x^2}}\,{\rm d}x{\rm,\ }0\leq\alpha<1.$$

{\bf 1$^\circ$. }\cyr{Ispitati neprekidnost funkcije }$I(\alpha)$.

{\bf 2$^\circ$. }\cyr{Proveriti: }
$$\frac{{\rm d}I}{{\rm d}\alpha}
=\int_0^1\frac{1}{x\,\sqrt{1-x^2}}\Bigl(\frac{{\rm d}}{{\rm d\alpha}}
\ln(1-\alpha^2x^2)\Bigr)\,{\rm d}x{\rm,\ }0<\alpha<1.$$

{\bf 3$^\circ$. }\cyr{Na\'ci }$I(\alpha)$.

\bye