凡尘之外
幼苗
共回答了17个问题采纳率:82.4% 举报
∫dx/(x+根号1-x^2)
令x=sint
原式=∫cost/(sint+cost) dt
=1/2 ∫(cost-sint)/(sint+cost) dt+1/2 ∫(cost+sint)/(sint+cost) dt
=1/2∫1/(sint+cost) d(sint+cost)+1/2∫dt
=1/2ln|sint+cost|+1/2t+c
t=arcsinx
cost=√1-x^2
所以
原式=1/2ln|x+√1-x^2|+1/2arcsinx+c
1年前
12