求(x^3)*[e^(x^2)]的不定积分，谢谢

∫(x^3）[e^(x^2)]dx=∫(1/2)(x^2)[e^(x^2)]2xdx
=(1/2)∫(x^2)[e^(x^2)]d(x^2)
=(1/2)∫t(e^t)dt {令t=x^2}
=(1/2)[t(e^t)-∫(e^t)dt]
=(1/2)[t(e^t)-(e^t)]+C
=(1/2)(e^t)(t-1)+C
=(1/2)[e^(x^2)][(x^2)-1]+C
高数都忘得差不多啦，应该没错吧

采用分部积分法：

∫(x^3)·[e^(x^2)] dx

=1/2 ∫(x^2) d[e^(x^2)]

=1/2 (x^2)·[e^(x^2)] - 1/2 ∫[e^(x^2)] d(x^2)

=1/2 (x^2)·[e^(x^2)] - 1/2 e^(x^2) + C