How do you find $\int \frac{2 x}{x^{3} - x^{2} + x - 1} d x$ $int (2x)/(x^3-x^2+x-1)dx$ using partial fractions?

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Answer 1 · 2015-10-28T11:54:34

I found: $ln | x - 1 | + arctan (x) - \frac{1}{2} ln (x^{2} + 1) + c$ $ln|x-1|+arctan(x)-1/2ln(x^2+1)+c$

I had to do some manipulations (in the blue frames) and get:
enter image source here

How do you find int (2x)/(x^3-x^2+x-1)dx∫2xx3−x2+x−1dxint (2x)/(x^3-x^2+x-1)dx using partial fractions?