∫arctanx/x^2dx=-∫arctanxd(1/x)=-1/x*arctanx+∫1/x*1/(1+x²)dx=-arctanx/x+∫(1/x-x/(1+x²))dx=-arctanx/x+lnx-1/2∫1/(1+x²)d(1+x²)=-arctanx/x+lnx-1/2*ln(1+x²)+c