∫ dx/(x^2+1)^2 let x=tanu dx=(secu)^2 du ∫ dx/(x^2+1)^2 =∫ (cosu)^2 du =(1/2)∫ (1+cos2u) du =(1/2)[ u + (1/2)sin2u] +C =(1/2) [ arctanx + x/(x^2+1) ] +C
