令t=1/x
原式 = ∫ (arctant)/(1+ 1/t^2) d(1/t)
= - ∫ (arctant) / (t^2 +1) dt
= - ∫ arctant darctant
= -1/2(arctant)^2 +C
= -1/2 ( arctan 1/x )^2 +C