求不定积分∫xarctanxdx
1个回答
展开全部
∫ 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
= ∫ 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
本回答由提问者推荐
已赞过
已踩过<
评论
收起
你对这个回答的评价是？
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
