1. The solution set of the inequality $(x+1)^{3}\left(x^{3}+5 x\right)<10(x+1)^{2}$ +8 is
1. Solution: Let $f(x)=x^{3}+5 x$, then $f(x)$ is an increasing function on $\mathbf{R}$. When $x>-1$, the original inequality is $\left(\frac{2}{x+1}\right)^{3}+\frac{10}{x+1}>x^{3}+5 x$ which is equivalent to $f\left(\frac{2}{x+1}\right)>f(x) \Leftrightarrow \frac{2}{x+1}>x$. Solving this, we get $-1<x<1$;
When $x=-1$, the original inequality clearly holds;
When $x<-1$, the original inequality is $\left(\frac{2}{x+1}\right)^{3}+\frac{10}{x+1}<x^{3}+5 x \Leftrightarrow f\left(\frac{2}{x+1}\right)<f(x) \Leftrightarrow \frac{2}{x+1}<x$,
Solving this, we get $-2<x<-1$. In summary, the solution to the original inequality is $(-2,1)$.