=∫(arctanx)²d(x²/2) =(x²/2)(arctanx)²-∫x²arctanx/(x²+1)dx,设第一项为(*) =(*)-∫utan²xdu,u=arctanx =(*)-∫usec²udu+∫udu =(*)-(utanu-∫tanudu)+u²/2 =(*)-utanu-ln|cosu|+u²/2+C 将u代入即可。
