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

  • question_answer
    \[\int_{{}}^{{}}{[\sin (\log x)+\cos (\log x)]}\ dx=\]           [MP PET 1991]

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

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

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

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

    Correct Answer: D

    Solution :

     \[\int_{{}}^{{}}{\sin (\log x)\,dx}+\int_{{}}^{{}}{\cos (\log x)\,dx}\]                      \[=x\sin (\log x)-\int_{{}}^{{}}{\frac{x\cos (\log x)}{x}}\,dx+\int_{{}}^{{}}{\cos (\log x)\,dx+c}\]                      \[=x\sin (\log x)+c.\]


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