求积分:∫-ln(1-x)dx

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求积分:∫-ln(1-x)dx

求积分:∫-ln(1-x)dx
求积分:∫-ln(1-x)dx

求积分:∫-ln(1-x)dx
原式=∫ln(1-x)d(1-x)
=(1-x)ln(1-x)-∫(1-x)dln(1-x)
=(1-x)ln(1-x)-∫(1-x)*[-1/(1-x)]dx
=(1-x)ln(1-x)+∫dx
=(1-x)ln(1-x)+x+C

=(1-x)ln(1-x)-∫(1-x)dln(1-x)
=(1-x)ln(1-x)-∫(1-x)*[-1/(1-x)]dx
=(1-x)ln(1-x)+∫dx
=(1-x)ln(1-x)+x+C

∫-ln(1-x)dx
= ∫ln(1-x)d(1-x)
=(1-x)ln(1-x)-x+C

因为-XLn(1-X)的导数等于-Ln(1-X)+1/(1-X)-1则可通过添项求得原函数为-XLn(1-X)+Ln(1-X)+X+C