_ ^ x^4 + x^2 + 1 x^2 - x + 1 ;dx = - Vidyadip

MCQ

$\int_{}^{} {\frac{{{x^4} + {x^2} + 1}}{{{x^2} - x + 1}}\;dx = } $

✓
$\frac{1}{3}{x^3} + \frac{1}{2}{x^2} + x + c$
B
$\frac{1}{3}{x^3} - \frac{1}{2}{x^2} + x + c$
C
$\frac{1}{3}{x^3} + \frac{1}{2}{x^2} - x + c$
D
None of these

✓

Answer

Correct option: A.

$\frac{1}{3}{x^3} + \frac{1}{2}{x^2} + x + c$

a
(a)$\int_{}^{} {\frac{{{x^4} + {x^2} + 1}}{{{x^2} - x + 1}}\,dx} = \int_{}^{} {({x^2} + x + 1)\,dx} = \frac{{{x^3}}}{3} + \frac{{{x^2}}}{2} + x + c.$

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