原式=-∫arctanxd(1/x)
=-arctanx/x+∫1/x*1/(x^2+1)dx
=-arctanx/x+∫(1/x-x/(x^2+1))dx
=-arctanx/x+∫dx/x-1/2∫d(x^2+1)/(x^2+1)
=-arctanx/x+ln|x|-1/2ln|x^2+1|+C
=-arctanx/x+ln|x|-1/2ln(x^2+1)+C