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If $\int \frac{d x}{x^{4} - x^{2}} = \frac{1}{x} + \log | f (x) | + C$ then $f (x)$ is given by

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detailed solution

Correct option is C

1x4−x2=1x2(x−1)(x+1)=121x21x−1−1x+1=121x−1−1x−1x2−1x2−1x−1x+1=121x−1−2x2−1x+1∫dxx4−x2=12log⁡|x−1|−log⁡|x+1|+2x+C=1x+log⁡x−1x+11/2+C.

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If ∫dxx4−x2=1x+log⁡|f(x)|+C then f(x) is given by

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If $\int \frac{d x}{x^{4} - x^{2}} = \frac{1}{x} + \log | f (x) | + C$ then $f (x)$ is given by