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    The fraction =-1/x^2+1/(x^2+1)+1/2/(x-1)-1/2/(x+1)

    The integral = 1/x+arctan x+1/2 ln (x-1)-1/2ln(x+1) +c
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    The fraction =-1/x^2+1/(x^2+1)+1/2/(x-1)-1/2/(x+1)

    The integral = 1/x+arctan x+1/2 ln (x-1)-1/2ln(x+1) +c
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