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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Fundamental Integration

  • question_answer
    \[\int_{{}}^{{}}{\frac{{{x}^{4}}+{{x}^{2}}+1}{{{x}^{2}}-x+1}\ dx=}\]

    A)            \[\frac{1}{3}{{x}^{3}}+\frac{1}{2}{{x}^{2}}+x+c\]

    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

    Correct Answer: A

    Solution :

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


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