分部积分法：
原式=0.5∫ ln(1+x^2) d(-1/x^2)
=0.5[ -1/x^2*ln(1+x^2)+∫1/x^2*2x/(1+x^2)dx]
=0.5[-1/x^2*ln(1+x^2)+2∫1/x(1+x^2)dx]
=-0.5/x^2ln(1+x^2)-∫[1/x-x/(1+x^2)] dx
=-0.5/x^2 ln(1+x^2)-ln|x|+ 0.5ln(1+x^2)+C
求不定积分 ∫ ln(1+x^2)/x^3 dx 详细过程 谢谢
分部积分法：
原式=0.5∫ ln(1+x^2) d(-1/x^2)
=0.5[ -1/x^2*ln(1+x^2)+∫1/x^2*2x/(1+x^2)dx]
=0.5[-1/x^2*ln(1+x^2)+2∫1/x(1+x^2)dx]
=-0.5/x^2ln(1+x^2)-∫[1/x-x/(1+x^2)] dx
=-0.5/x^2 ln(1+x^2)-ln|x|+ 0.5ln(1+x^2)+C