The value(s) of ₀^1 x^4(1-x)^4 1+x^2 d x is (are)

Step-by-step solution

Let I= ₀^1 x^4(1-x)^4 1+x^2 d x aligned & = ₀^1 (x^4-1 )(1-x)^4+(1-x)^4 (1+x^2 ) d x & = ₀^1 (x^2-1 )(1-x)^4 d x & + ₀^1 (1+x^2-2 x )^2 (1+x^2 ) d x & = ₀^1 (x^2-1 )(1-x)^4+ (1+x^2 )-4 x . & .+ 4 x^2 (1+x^2 ) d x & = ₀^1 ( (x^2-1 )(1-x)^4+ (1+x^2 )-4 x . & .+4- 4 1-x^2 ) d x & = ₀^1 (x^6-4 x^5+5 x^4-4 x^2 . & .+4- 4 1+x^2 ) d x & = [ x^7 7 - 4 x^6 6 + 5 x^5 5 . & aligned aligned & . - 4 x^3 3 +4 x-4 ⁻¹ x ]₀^1 = & 1 7 - 4 6 + 5 5 - 4 3 +4-4 ( 4 -0 ) = & 22 7 - aligned