If $\text{⨍ }\left(\mathrm{x}\right){\text{=x}}^3{\text{+ax}}^2{\text{+bx+5sin}}^2$ is an incresing function on R, then

$$\begin{gathered} {\text{⨍ (x)=x}}^3{\text{+ax}}^2{\text{+bx+5sin}}^2\text{x} \\ {\text{⨍ }}^1{\text{(x)=3x}}^2\text{+2ax+b+10sin x cos x} \\ =3{\mathrm{x}}^2+2\mathrm{ax}+\mathrm{b}+5 \sin 2\mathrm{x} \\ {\text{⨍ }}^{11}\text{(x)=6x+2a+10 cos2x} \\ {\text{⨍ }}^{11}\text{(x)=6-20 sin2x} \\ \text{⨍ (x)=6-20 sin2x} \end{gathered}$$

$\text{⨍ (x)}$ is increasing

$$\begin{gathered} \Rightarrow {\text{⨍ }}^1\text{(x)>0} \\ \Rightarrow {\text{⨍ }}^{111}\text{(x)>0} \\ \sin 2\mathrm{x}=1 \\ {\text{⨍ }}^1{\text{(x)=3x}}^2\text{+2ax+b-5>0} \\ 4{\mathrm{a}}^2-4\left(3\right) (\mathrm{b}-5)<0 \\ {\mathrm{a}}^2-3\mathrm{b}+15<0 \end{gathered}$$