设x=sint,t=arcsinx,dx=costdt,
原式=∫(sint)^2*costdt/cost
=∫(sint)^2dt
=(1/2)∫(1-cos2t)dt
=t/2-(1/4)sin2t+C
=(arcsinx)/2-(1/2)x√(1-x^2)+C.
求∫(x2/(√(1-x2)dx的不定积分
设x=sint,t=arcsinx,dx=costdt,
原式=∫(sint)^2*costdt/cost
=∫(sint)^2dt
=(1/2)∫(1-cos2t)dt
=t/2-(1/4)sin2t+C
=(arcsinx)/2-(1/2)x√(1-x^2)+C.