搜搜做题作业网求不定积分,见图
来源：学生作业帮 编辑：搜搜做题作业网作业帮 分类：数学作业 时间：2024/06/23 22:43:13
求不定积分,见图
x=sint,√(1-x^2) = cost,dx = cost dt
原式= ∫ cost/(sint+cost) dt
= (1/2) ∫ [ 1 + (cost-sint)/(sint+cost)] dt
= (1/2) [ 1 + ln(sint + cost) ] + C
= (1/2)arcsinx + (1/2) ln( x+ √(1-x^2) ) + C
原式= ∫ cost/(sint+cost) dt
= (1/2) ∫ [ 1 + (cost-sint)/(sint+cost)] dt
= (1/2) [ 1 + ln(sint + cost) ] + C
= (1/2)arcsinx + (1/2) ln( x+ √(1-x^2) ) + C