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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Integration by Substitution

  • question_answer
    \[\int_{{}}^{{}}{\frac{1}{x}{{\sec }^{2}}(\log x)dx=}\]

    A)            \[\tan (\log x)+c\]

    B)            \[\log (\sec x)+c\]

    C)            \[\log (\tan x)+c\]

    D)            \[\sec (\log x)\ .\ \tan (\log x)+c\]

    Correct Answer: A

    Solution :

                       Put \[t=\log x\Rightarrow x\,dt=dx,\] then            \[\int_{{}}^{{}}{\frac{1}{x}{{\sec }^{2}}(\log x)\,dx}=\int_{{}}^{{}}{{{\sec }^{2}}t\,dt=\tan t+c}=\tan (\log x)+c\].


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