Question

∫sin(3√x)dx

3√x是x开三次

Answer 1

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

Answer 2

∫sin(3√x)dx=cos(3√x)(1-2/3√x)+c

追问

cos(3√x)(1-2/3√x)是cos(3√x)*(1-2/3√x)还是cos[(3√x)(1-2/3√x)]
还有过程，亲~