1/(x^2+1)^2 =(1/2) ( (1-x^2)/(x^2+1)^2 +(1+x^2)/(x^2+1)^2 )
=(1/2) ( ((x^2+1)-x(2x))/(x^2+1)^2 +1/(x^2+1) )
=(1/2) ( (x/(x^2+1))' + (arctan(x))' )

∫1/(x^2+1)^2 dx=(1/2)( x/(x^2+1) +arctan(x) ) +C