If ∫$$(2x$$−$$1)dxx4$$−$$2x3+x+1=Atan$$−$$1$$⁡$$f(x)3+C$$ then

Correct option is 3f(x)=2x2−2x−1

Questions

$If \int \frac{(2 x - 1) dx}{x^{4} - 2 x^{3} + x + 1} = {Atan}^{- 1} [\frac{f (x)}{\sqrt{3}}] + C$ then

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A=13

A=2

f(x)=2x2−2x−1

f(x)=2x2+2x+1

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detailed solution

Correct option is C

I=∫(2x−1)dxx2−x2−x2−x+1 Put x2−x=tI=∫dtt2−t+1=∫dtt−122+34I=∫dtt−122+322⇒I=23tan−1⁡2x2−2x−13+C

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If ∫(2x−1)dxx4−2x3+x+1=Atan−1⁡f(x)3+C then

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$If \int \frac{(2 x - 1) dx}{x^{4} - 2 x^{3} + x + 1} = {Atan}^{- 1} [\frac{f (x)}{\sqrt{3}}] + C$ then