$$ \mathop {\lim }\limits_{x \to 1}\left(\log _3 3 x\right)^{\log _x 8}=\ldots $$

The function $\mathrm{f}(x)=\sin ^4 x+\cos ^4 x$ increases if

The values of $b$ and $c$ for which the identity $\mathrm{f}(x+1)-\mathrm{f}(x)=8 x+3$ is satisfied, where $\mathrm{f}(x)=\mathrm{b} x^2+\mathrm{c} x+\mathrm{d}$, are

$$ \int \frac{x^3}{x^4+5 x^2+4} d x= $$