1.Prove

${\displaystyle {\frac {x^{4}(1-x)^{4}}{1+x^{2}}}>=0}$

2.Find A to H

${\displaystyle {\frac {x^{4}(1-x)^{4}}{1+x^{2}}}=Ax^{6}+Bx^{5}+Cx^{4}+Dx^{3}+Ex^{2}+Fx+G+{\frac {H}{1+x^{2}}}}$

3. Find

${\displaystyle \int _{0}^{1}{\frac {x^{4}(1-x)^{4}}{1+x^{2}}}\,dx}$

Given

${\displaystyle {\frac {d}{dx}}\arctan {x}\ ={\frac {1}{1+x^{2}}}\ }$

4.Prove

${\displaystyle {\frac {22}{7}}>\pi }$