Question

integrate (x^2 - 1)/(x^2 + 1)^2

Answer 1

-1/(+1)^2
-1 can be written as +1-2
now splitting denominator 
+1 / (+1)^2  +2 /(+1)^2
 on dividing (+1)/(+1)^2 we get  1/.(+1)
now we are left with
1/(+1) dx +2/(+1)^2dx
now integrating  we get
 x - 2/(+1)+C.....................as iintegration of1/ (+a) is
 (1/a  x/a)
and for  integration of 1/(+1) ^2
let say (+1)=t
so integration of (+1)^2
is like 1/ which is  and its integration is /-2+1
and now substituting the value we get our answer as
 x - 2/(+1)+C...
where c is a constant