∫sin(3√x)dx

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