Question

求(x^3)*[e^(x^2)]的不定积分,谢谢

Answer 1

∫(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