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求助不定积分计算∫3x^2e^xdx

求助不定积分计算∫3x^2e^xdx,要详细过程.

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可用分部积分法:

∫ 3x²e^x dx

= 3∫ x² d(e^x)

= 3x²e^x - 3∫ e^x d(x²)

= 3x²e^x - 3∫ 2xe^x dx

= 3x²e^x - 6∫ x d(e^x)

= 3x²e^x - 6xe^x + 6∫ e^x dx

= 3x²e^x - 6xe^x + 6e^x + C

= 3(x² - 2x + 2)e^x + C

1年前

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