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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Self Evaluation Test - Integrals

  • question_answer
    \[\int{{{e}^{3\log x}}{{({{x}^{4}}+1)}^{-1}}dx}\] is equal to

    A) \[\log ({{x}^{4}}+1)+C\]

    B) \[\frac{1}{4}\log ({{x}^{4}}+1)+C\]

    C) \[-\log ({{x}^{4}}+1)+C\]

    D) None of these

    Correct Answer: B

    Solution :

    [b] \[\int{{{e}^{3\,\,\log \,\,x}}{{({{x}^{4}}+1)}^{-1}}dx=\int{{{e}^{\log \,\,{{x}^{3}}}}\frac{1}{{{x}^{4}}+1}dx}}\] \[=\int{\frac{{{x}^{3}}}{{{x}^{4}}+1}dx=\frac{1}{4}\log ({{x}^{4}}+1)+C}\] [since \[{{e}^{\log \,\,{{x}^{3}}}}={{x}^{3}}\]]


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