计算不定积分∫x^21n xdx

问题描述:

计算不定积分∫x^21n xdx
1个回答 分类:数学 2014-10-25

问题解答:

我来补答
∫x²lnx dx,宜用分部积分法
= (1/3)∫lnx d(x³)
= (1/3)x³lnx - (1/3)∫x³ d(lnx)
= (1/3)x³lnx - (1/3)∫x² dx
= (1/3)x³lnx - (1/9)x³ + C
= (1/9)x³(3lnx-1) + C
 
 
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