先算不定积分,分部积分=x ln (1+x^2)-∫ x*2x/(1+x^2)dx=x ln(1+x^2)-2∫ [1-1/(1+x^2)]dx=xln(1+x^2)-2x+2 arctan x代入x=1,得到 ln2-2+2*pi/4x=e,e*ln(1+e^2)-2*e+2*arctan e后者减前者=[e*ln(1+e^2)-2*e+2*arctan...