2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Indefinite Integrals

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

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

    A)            \[\log \cos (\log x)+c\]

    B)            \[\log \sin (\log x)+c\]

    C)            \[\log \sec (\log x)+c\]

    D)            \[\log \text{cosec}(\log x)+c\]

    Correct Answer: C

    Solution :

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


You need to login to perform this action.
You will be redirected in 3 sec spinner