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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Integration of Rational Function by Using Partial Fractions

  • question_answer
    \[\int_{{}}^{{}}{\frac{dx}{(x+1)(x+2)}=}\]                 [MP PET 1987]

    A)                 \[\log \frac{x+2}{x+1}+c\]

    B)                 \[\log (x+1)+\log (x+2)+c\]

    C)                 \[\log \frac{x+1}{x+2}+c\]

    D)                 None of these

    Correct Answer: C

    Solution :

                       \[\int_{{}}^{{}}{\frac{dx}{(x+1)(x+2)}}=\int_{{}}^{{}}{\left( \frac{1}{x+1}-\frac{1}{x+2} \right)}\,dx\]                                 \[=\log (x+1)-\log (x+2)+c=\log \frac{x+1}{x+2}+c.\]


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