分部积分法，原函数＝(1/2)x²arctanx - ∫(1/2)x² d(arctanx)＝(1/2)x²arctanx - (1/2) ∫ [1 - 1/(1＋x²)]dx＝(1/2)x²arctanx - x/2＋arctanx / 2所以原式＝π/8 - 1/2＋π/8＝π/4 - 1/2
