indefinite-integration

Question: $\int_{{}}^{{}}{\frac{1}{(x-1)({{x}^{2}}+1)}dx}=$

1) $\frac{1}{2}\log (x-1)-\frac{1}{4}\log ({{x}^{2}}+1)-\frac{1}{2}{{\tan }^{-1}}x+c$

2) $\frac{1}{2}\log (x-1)+\frac{1}{4}\log ({{x}^{2}}+1)-\frac{1}{2}{{\tan }^{-1}}x+c$

3) $\frac{1}{2}\log (x-1)-\frac{1}{2}\log ({{x}^{2}}+1)-\frac{1}{2}{{\tan }^{-1}}x+c$

4) None of these

Solution:

Explanation: No Explanation

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