计算不定积分∫x^21n xdx

分类: 作业答案 • 2022-01-09 18:03:57

问题描述：

计算不定积分∫x^21n xdx

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...