求下列不定积分

Question

求下列不定积分不定积分

Answer 1

望采纳谢谢啦

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Answer 2

令 x^(1/3) = u, 则 x = u^3, dx = 3u^2du
I = ∫ 3u^2 e^u du = 3 ∫ u^2 d(e^u)
= 3u^2e^u - 3∫2ue^udu = 3u^2e^u - 6∫ud(e^u)
= 3u^2e^u - 6ue^u + 6∫e^udu
= 3u^2e^u - 6ue^u + 6e^u + C
= 3e^[x^(1/3)][ x^(2/3)-2x^(1/3)+2] + C