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求不定积分∫lnx/x^1/2dx
题目详情
求不定积分∫ lnx / x^1/2 dx
▼优质解答
答案和解析
∫ lnx / x^1/2 dx
=2∫lnxd[x^(1/2)],利用分步积分得到：
=2lnx*x^(1/2)-2∫x^(1/2)dlnx
=2x^(1/2)lnx-2∫x^(1/2)/x dx
=2x^(1/2)lnx-2∫x^(-1/2)dx
=2x^(1/2)lnx-4x^(1/2)+c
=2∫lnxd[x^(1/2)],利用分步积分得到：
=2lnx*x^(1/2)-2∫x^(1/2)dlnx
=2x^(1/2)lnx-2∫x^(1/2)/x dx
=2x^(1/2)lnx-2∫x^(-1/2)dx
=2x^(1/2)lnx-4x^(1/2)+c
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