求解高等数学题,过程详细求x^3e^(-x^2)的不定积分
2019-04-14
求解高等数学题,过程详细
求x^3e^(-x^2)的不定积分
优质解答
∫(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
= ……
∫(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
= ……