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

  • question_answer
    \[\int_{{}}^{{}}{\log xdx=}\]        [MNR 1979; BIT Ranchi 1992; SCRA 1996]

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

    B)                 \[x\log x-x+c\]

    C)                 \[{{x}^{2}}\log x+c\]

    D)                 \[\frac{1}{x}\log x+x+c\]

    Correct Answer: B

    Solution :

                    \[\int_{{}}^{{}}{\log x\,dx}=x\log x-\int_{{}}^{{}}{x\,.\,\frac{1}{x}\,dx+c=x\log x-x+c}\]                 Note : Students should remember this question as a formula.


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