Evaluate: `intx/((x^2+1)(x-1))\ dx`

Explanation

Let `I=int frac{x}{(x^{2}+1)(x-1)} d x`

We express



`frac{x}{(x^{2}+1)(x-1)}=frac{A}{x-1}+frac{B x+C}{x^{2}+1} `

`Rightarrow x=A(x^{2}+1)+(B x+C)(x-1)`

Equating the coefficients of `x^{2}, x` and constants, we get

`0=A+B` and `1=-B+C` and `0=A-C` or `A=frac{1}{2}` and `B=-frac{1}{2}` and `C=frac{1}{2}`

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