求积分∫√x/(1-√x次方)dx

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求积分∫√x/(1-√x次方)dx求积分∫√x/(1-√x次方)dx求积分∫√x/(1-√x次方)dx令t²=x,2tdt=dx∫√x/(1-√x)dx=2∫t²/(1-t)dt=

求积分∫√x/(1-√x次方)dx
求积分∫√x/(1-√x次方)dx

求积分∫√x/(1-√x次方)dx
令t² = x,2t dt = dx
∫ √x/(1 - √x) dx
= 2∫ t²/(1 - t) dt
= - 2∫ t²/(t - 1) dt
= - 2∫ [(t² - 1) + 1]/(t - 1) dt
= - 2∫ (t + 1) dt - 2∫ dt/(t - 1)
= - 2(t²/2 + t) - 2ln|t - 1| + C
= - x - 2√x - 2ln|1 - √x| + C