If $\frac{x+1}{(x-1)^2\left(x^2+1\right)}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C x+D}{x^2+1}$, then $\sqrt{3 A^2+4 D^2+5 C^2+B^2}=$

$$ \int \frac{1}{9 \cos ^2 x-24 \sin x \cos x+16 \sin ^2 x} d x= $$

If $\int \frac{1}{\cot \frac{x}{2} \cot \frac{x}{3} \cot \frac{x}{6}} d x=A \log \left|\cos \frac{x}{2}\right| +B \log \left|\cos \frac{x}{3}\right|+C \log \left|\cos \frac{x}{6}\right|+k$, then $A+B+C=$

$$ \int \frac{\sin x+\cos x}{\sin x-\cos x} d x= $$