If $\lim \limits_{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{4}{n^2}\right)\left(1+\frac{9}{n^2}\right) \ldots\left(1+\frac{n^2}{n^2}\right)\right]^{\frac{1}{n}}=a e^b$, then $$ a+b= $$

$$ \int_0^\pi x \sin ^4 x \cos ^6 x d x= $$

If $I_n=\int_0^{\frac{\pi}{4}} \tan ^n x d x$, then $I_{13}+I_{11}=$

$\lim \limits_{n \rightarrow+\infty}\left[{\frac{1}{n^4}+\frac{1}{\left(n^2+1\right)^{\frac{3}{2}}}+\frac{1}{\left(n^2+4\right)^{\frac{3}{2}}}+\frac{1}{\left(n^2+9\right)^{\frac{3}{2}}}}{+\ldots \ldots+\frac{1}{4 \sqrt{2} n^5}}\right]=$