User:GrigorIII

1.Prove

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

2.Find A to H

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

3. Find

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

Given

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

4.Prove

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