x*[ln(1+x)/(1-x)]d的不定积分

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x*[ln(1+x)/(1-x)]d的不定积分

x*[ln(1+x)/(1-x)]d的不定积分
x*[ln(1+x)/(1-x)]d的不定积分

x*[ln(1+x)/(1-x)]d的不定积分
∫ xln[(1+x)/(1-x)] dx
=(1/2)∫ ln[(1+x)/(1-x)] dx^2
= (1/2)x^2ln[(1+x)/(1-x)] - (1/2) ∫ [x^2/(1+x) +x^2/(1-x) ]dx
=(1/2)x^2ln[(1+x)/(1-x)] - (1/2) ∫ [ x-1 +1/(1+x) -x -1 +1/(1-x) ]dx
=(1/2)x^2ln[(1+x)/(1-x)] - (1/2) ∫ [ -2 +1/(1+x) +1/(1-x) ]dx
=(1/2)x^2ln[(1+x)/(1-x)] + x - ln|(1+x)/(1-x)| + C