Spo�t�te
$$
\gather
\lim_{n \to +\infty}\int_0^1\frac{x^n}{n} \dx, \qquad
\lim_{n \to +\infty}\int_0^1\frac{\sqrt{n^3}x}{1+n^2x^2} \dx,
\qquad
\lim_{n \to +\infty}\int_0^1\frac{x^n}{1+x^{2n}} \dx \quad .
\endgather
$$
