xarctanx定积分∫x*arctanxdx=∫arctanxd(x²/2)=(x²/2)arctanx-(1/2)∫x²d(arctanx)=(x²/2)arctanx-(1/2)∫x²/(x²+1)dx=(x²/2)arctanx-(1/2)∫(x²+1-1)/(x²+1)dx=(x²/2)arct

Question

xarctanx定积分
∫ x * arctanx dx
= ∫ arctanx d(x²/2)
= (x²/2)arctanx - (1/2)∫ x² d(arctanx)
= (x²/2)arctanx - (1/2)∫ x²/(x² + 1) dx
= (x²/2)arctanx - (1/2)∫ (x² + 1 - 1)/(x² + 1) dx
= (x²/2)arctanx - (1/2)∫ dx + (1/2)∫ dx/(x² + 1)
= (x²/2)arctanx - x/2 + (1/2)arctanx + C
倒数第二三步看不懂

Answer 1

用的是拆项呀,有什么不懂的