Question

help me

Answer 1

\[\int\limits_{0}^{1}(x)^4(1-x)^4/(1+x^2)\]

Answer 2

you could do long division on the first term
this will give
x^6 - x^4 - 4x^2 + 4 - 4 /(1 + x^2)
so substituting for the first term we get:-
x^6 - 4x^5 + 5x^4 - 4x^2 + 4 - 4/(1+x^2)

so integrate term by term - the last term is a standard integral - if my memory serves me right the integral is -4 arctan x