how to integrate (-4)/ ((x^2 +2x+2)^2) ? thxxxx?

Sol
x^2+2x+2=(x+1)^2+1
Set x+1=Tanw
w=ArcTan(x+1)
SinwCosw=(x+1)/(x^2+2x+2)
x^2+2x+2=sec^2 w
dx=Sec^2 wdw
∫－4dx/(x^2+2x+2)^2
=∫－4Sec^2 w/sec^4 w
=∫－4Cos^2 wdw
=∫－2(1+Cos2w)dw
=－2∫dw－∫Cos2wd(2w)
=－2w+Sin(2w)+c
=－2ArcTan(x+1)+2(x+1)/(x^2+2x+2)+c