2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Indefinite Integrals

JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Fundamental Integration

  • question_answer
    \[\int_{{}}^{{}}{\frac{{{x}^{2}}+x-6}{(x-2)(x-1)}dx=}\]

    A)            \[x+2\log (x-1)+c\]

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

    C)            \[x+4\log (1-x)+c\]

    D)            \[x+4\log (x-1)+c\]

    Correct Answer: D

    Solution :

               \[\int_{{}}^{{}}{\frac{{{x}^{2}}+x-6}{(x-2)(x-1)}\,dx}=\int_{{}}^{{}}{\frac{(x+3)(x-2)}{(x-2)(x-1)}\,dx}=\int_{{}}^{{}}{\frac{x+3}{x-1}\,dx}\]                    \[=\int_{{}}^{{}}{\frac{x-1}{x-1}\,dx+\int_{{}}^{{}}{\frac{4}{x-1}\,dx}}=x+4\log (x-1)+c\].


You need to login to perform this action.
You will be redirected in 3 sec spinner