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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Integration of Rational Function by Using Partial Fractions

  • question_answer
    \[\int{\frac{dx}{{{x}^{2}}+4x+13}}\] is equal to                                     [Kerala (Engg.) 2002]

    A)                 \[\log ({{x}^{2}}+4x+13)+c\]

    B)                 \[\frac{1}{3}{{\tan }^{-1}}\left( \frac{x+2}{3} \right)+c\]

    C)                 \[\log (2x+4)+c\]

    D)                 \[\frac{2x+4}{{{({{x}^{2}}+4x+13)}^{2}}}+c\]

    Correct Answer: B

    Solution :

                    \[\int{\frac{dx}{{{x}^{2}}+4x+13}=\int{\frac{dx}{{{(x+2)}^{2}}+9}=\frac{1}{3}{{\tan }^{-1}}\frac{(x+2)}{3}+c}}\].


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