Primitive of 3 x^ 4 , - 1 ( x^4 + x + 1) ^2 w.r.t. x is : - Vidyadip

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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