求不定积分：∫arcsinx/(1-x2)3/2dx

求不定积分：
∫arcsinx/(1-x²)^3/2dx
【正确答案】：令arcsinx=t,x=sint,dx=costdt,则 ∫arcsinx/(1-x²)^3/2dx=∫t/cos³·costdt =∫tsec²tdt=∫tdtant =ttant-∫tan=tdt =ttant+∫1/costdcost =ttant+lncost+C =tsint/√(1-sin²t)+ln√(1-sin²t)+C =xarcsinx/√(1-x²)+ln√(1-x²)+C