$$ \lim _{n \rightarrow \infty}\left[\begin{array}{c} \frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4}{n^2}+\frac{3}{n^2} \sec ^2 \\ \frac{9}{n^2}+\ldots+\frac{1}{n^2} \sec ^2 1 \end{array}\right]= $$

$$ \int_0^\pi\left(\sin ^5 x \cos ^3 x+\sin ^4 x \cos ^4 x+\sin ^3 x \cos ^4 x\right) d x= $$

$$ \int_0^1 \frac{x^4+1}{x^6+1} d x= $$

$$ \int_{-2 \pi}^{2 \pi} \sin ^4(2 x) \cos ^6(2 x) d x= $$