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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
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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