=((x-1)^2 (x+1)^2)\/(4 x (a x+x^2+1))
=(x^4-2 x^2+1)\/(4 a x^2+4 x^3+4 x)
x = 1, a - 2=/0
x = 1, a + 2=/0
={x element R : (a<=-2 and x<0) or (a<=-2 and x>0 and sqrt(a^2-4)+a+2 x<0)
or (a<=-2 and sqrt(a^2-4)+a+2 x>0 and sqrt(a^2-4)>a+2 x)
or (a<=-2 and a+2 x>sqrt(a^2-4))
or (-2
or (a>=2 and sqrt(a^2-4)
or (a>=2 and sqrt(a^2-4)+a+2 x<0)}
1\/(4 x)-a\/4+1\/4 (a^2-3) x+(a-a^3\/4) x^2+1\/4 (a^4-5 a^2+4) x^3+O(x^4)\n(Laurent series)
x\/4-a\/4+(a^2-3)\/(4 x)+(a-a^3\/4)\/x^2+O((1\/x)^3)\n
(d)\/(dx)((x^2-1)^2\/(4 x (x^2+a x+1))) = ((x^2-1) (2 a (x^3+x)+x^4+6 x^2+1))\/(4 x^2 (a x+x^2+1)^2)
integral (-1+x^2)^2\/(4 x (1+a x+x^2)) dx = 1\/8 ((a^2-4) log(a x+x^2+1)+2 a sqrt(4-a^2) tan^(-1)((a+2 x)\/sqrt(4-a^2))-2 a x+x^2+2 log(x))+constant
BTC: 199hWWjMZdZ59dfyKpi7AG7wKv9LnqJSij
please check your messages form me ive finished this bounty thanks!
