`(x^2+1/(x^2)+2)+(x^4+1/(x^4)+5)+(x^6+1/(x^6)+8)+`

If the coefficient of x^8 in the expansion of (1+ (x^2)/( 2!) + (x^4)/( 4!) + (x^6)/( 6!) + (x^8)/( 8!))^(2) is (1)/(M) , then a divisor of M is

(x^(2)+(1)/(x^(2)))-4(x+(1)/(x))+6

The coefficient of x^8 in the expasnsion of (1+(x^2)/(2!)+(x^4)/(4!)+(x^6)/(6!)+(x^8)/(8!))^2 is

1/(x^2-3x+2)+1/(x^2-5x+6)+1/(x^2-4x+3)

The series expansion of log[(1 + x)^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]

The series expansion of log_(e) [(1 + x^((1 + x))(1-x)^(1-x)] is (1) 2[(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (2) [(x^(2))/(1.2) + (x^(4))/(3.4)+(x^(6))/(5.6)+...] (3) 2[(x^(2))/(1.2) + (x^(4))/(2.3)+(x^(6))/(3.4)+...] (4) 2[(x^(2))/(1.2) -(x^(4))/(2.3)+(x^(6))/(3.4)-...]

The coefficient of x^(8) in the expasnsion of (1+(x^(2))/(2!)+(x^(4))/(4!)+(x^(6))/(6!)+(x^(8))/(8!))^(2) is