1个回答
展开全部
换元x＝sint，则dx＝costdt，原式＝∫costdt/(sint+cost)
cost/(sint+cost)＝1/2×(cost+sint+cost-sint)/(sint+cost)＝1/2×[1＋(cost-sint)/(sint+cost)]
所以，原式＝∫costdt/(sint+cost)＝1/2×∫[1＋(cost-sint)/(sint+cost)]dt＝1/2×[t＋∫1/(sint+cost)d(sint+cost)]＝1/2×[t＋ln|sint+cost|]＋C＝1/2×[arcsinx＋ln|(x＋√(1-x^2)|]＋C
cost/(sint+cost)＝1/2×(cost+sint+cost-sint)/(sint+cost)＝1/2×[1＋(cost-sint)/(sint+cost)]
所以，原式＝∫costdt/(sint+cost)＝1/2×∫[1＋(cost-sint)/(sint+cost)]dt＝1/2×[t＋∫1/(sint+cost)d(sint+cost)]＝1/2×[t＋ln|sint+cost|]＋C＝1/2×[arcsinx＋ln|(x＋√(1-x^2)|]＋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
