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

  • question_answer
    To find the value of \[\int_{{}}^{{}}{\frac{1+\log x}{x}\text{ }}dx\], the proper substitution is           [MP PET 1988]

    A)            \[\log x=t\]

    B)            \[1+\log x=t\]

    C)            \[\frac{1}{x}=t\]

    D)            None of these

    Correct Answer: B

    Solution :

                       Let \[1+\log x=t\Rightarrow \frac{1}{x}\,dx=dt\]            Therefore, \[\int_{{}}^{{}}{\frac{1+\log x}{x}}\,dx=\int_{{}}^{{}}{t\,dt}=\frac{{{t}^{2}}}{2}\]\[=\frac{{{(1+\log x)}^{2}}}{2}\].


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