>>242
(x^4+2x^2+1)/(x^4-2x^2+1)
=1 +(4x^2)/(x^4-2x^2+1)
=1 +x/(x^2-2x+1) -x/(x^2+2x+1)
=1 +(1/2)(2x-2)/(x^2-2x+1) +1/(x^2-2x+1) -(1/2)(2x+2)(x^2+2x+1) +1/(x^2+2x+1)
それぞれ、
∫dx=x
∫(2x-2)/(x^2-2x+1) dx=log|x^2-2x+1|
∫dx/(x-1)^2=-1/(x-1)
∫(2x+2)/(x^2+2x+1)dx=log|x^2+2x+1|
∫dx/(x+1)^2=-1/(x+1)
で積分できる。