2. 考研
  3. 计算∫[1nf(x)+lnf’(x)][f’2(x)+f(x)f”(x)]dx．

计算∫[1nf(x)+lnf’(x)][f’2(x)+f(x)f”(x)]dx．

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问题 计算∫[1nf(x)+lnf’(x)][f’2(x)+f(x)f”(x)]dx．
选项
答案原式=∫ln[f(x)f’(x)]d[f(x)f’(x)] =f(x)f’(x)·ln[f(x)f’(x)]-[*]d[f(x)f’(x)] =f(x)-f’(x)[ln[f(x)f’(x)]-1]+C．
解析
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考研数学二

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