求不定积分,arcsinx⼀根号[(1-x^2)^3]

2025-05-09 13:21:00
推荐回答(3个)
回答1:

换元t=arcsinx
=∫t/cos³tdsint
=∫tdtant
=ttant-∫tantdt
=ttant+ln|cost|+C

回答2:

回答3:

令x=sint,dx=costdt
原式=∫t/cos²tdt
=∫tdtant
=ttant-∫tantdt
=ttant-∫sint/costdt
=ttant-∫1/costdcost
=ttant-ln|cost|+C