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

  • question_answer
    \[\int_{{}}^{{}}{{{e}^{x}}\left[ \frac{1+x\log x}{x} \right]\ dx=}\]

    A)                 \[{{e}^{x}}+\log x+c\]

    B)                 \[\frac{{{e}^{x}}}{\log x}+c\]

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

    D)                 \[{{e}^{x}}\log x+c\]

    Correct Answer: D

    Solution :

                    \[\int_{{}}^{{}}{{{e}^{x}}\left[ \frac{1+x\log x}{x} \right]\,dx=}\int_{{}}^{{}}{{{e}^{x}}\left( \log x+\frac{1}{x} \right)\,dx}={{e}^{x}}\log x+c\].


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