Question

求解高等数学题,过程详细求x^3e^(-x^2)的不定积分

Answer 1

∫(x^3)[e^(-x^2)]dx

= (1/2)∫(x^2)[e^(-x^2)]d(x^2)

= (1/2)∫t[e^(-t)]dt (t = x^2)

= (-1/2)∫td[e^(-t)]

= (-1/2){te^(-t) - ∫[e^(-t)]dt} (分部积分法)

= (-1/2){te^(-t) + [e^(-t)]} + C

= ……