=-∫ln(x²+1)d(1/x)=-ln(x²+1)/x+∫(1/x)(2x/(x²+1))dx=-ln(x²+1)/x+2arctanxlimln(x²+1)/x=lim2x/(x²+1)=0=0+π-(-ln2+π/2)=ln2+π/2
