求∫x^3/√(1-x^2)dx的不定积分

答：
设x=sint
∫ x³ /√(1-x²) dx
=∫ sin³t /cost d(sint)
=∫ sin³t dt
=∫ sint(1-cos²t ) dt
=∫ (cos²t-1) d(cost)
=(1/3)cos³t -cost +C
=(1/3)(1-x²)√(1-x²)-√(1-x²)+C
=(-1/3)(2+x²)√(1-x²)+C