JCECE Engineering JCECE Engineering Solved Paper-2008

  • question_answer
    \[\int{\frac{dx}{{{x}^{2}}+4x+13}}\]is equal to

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

    Correct Answer: B

    Solution :

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


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