令³√x=t,那么x=t^3,
用分部积分法来慢慢做,但要细心
原积分
=∫ sint d(t^3)
=∫ 3t^2 *sint dt
= -3t^2 *cost + ∫ cost *d(3t^2)
= -3t^2 *cost + ∫ 6t *cost dt
= -3t^2 *cost + ∫ 6t d(sint)
= -3t^2 *cost + 6t *sint - ∫ 6sint dt
= -3t^2 *cost + 6t *sint +6cost +C
= -3³√x² *cos³√x + 6³√x *sin³√x +6cos³√x +C,C为常数