MCQ
Primitive of $\frac{{3{x^{4\,}} - 1}}{{{{({x^4} + x + 1)}^2}}}$ w.r.t.  $x$ is :
  • A
    $\frac{x}{{{x^4}\,\, + \,\,x\,\, + \,\,1}}$ $+ c$
  • $-$ $\frac{x}{{{x^4}\,\, + \,\,x\,\, + \,\,1}}$  $+$ $ c$ 
  • C
    $\frac{{x\,\, + \,\,1}}{{{x^4}\,\, + \,\,x\,\, + \,\,1}}$ $+ $ $c$
  • D
    $-$ $\frac{{x\,\, + \,\,1}}{{{x^4}\,\, + \,\,x\,\, + \,\,1}}$ $+$ $ c$ 

Answer

Correct option: B.
$-$ $\frac{x}{{{x^4}\,\, + \,\,x\,\, + \,\,1}}$  $+$ $ c$ 
b
$\frac{{3\,{x^4}\,\, - \,\,1}}{{{x^2}\,\,{{\left( {{x^3}\,\, + \,\,1\,\, + \,\,{x^{ - 1}}} \right)}^2}}}$=$ \frac{{3\,{x^2}\,\, - \,\,{x^{ - 2}}}}{{{{\left( {{x^3}\,\, + \,\,1\,\, + \,\,{x^{ - 1}}} \right)}^2}}}$

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