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

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

  • question_answer
    \[\int_{{}}^{{}}{{{e}^{-x}}\text{cose}{{\text{c}}^{2}}(2{{e}^{-x}}+5)}\ dx=\]        [AISSE 1988]

    A)            \[\frac{1}{2}\cot (2{{e}^{-x}}+5)+c\]

    B)            \[-\frac{1}{2}\cot (2{{e}^{-x}}+5)+c\]

    C)            \[2\cot (2{{e}^{-x}}+5)+c\]

    D)            \[-2\cot (2{{e}^{-x}}+5)+c\]

    Correct Answer: A

    Solution :

                       Put \[2{{e}^{-x}}+5=t\Rightarrow -2{{e}^{-x}}dx=dt,\] then            \[\int_{{}}^{{}}{{{e}^{-x}}\text{cose}{{\text{c}}^{\text{2}}}(2{{e}^{-x}}+5)\,dx}=-\frac{1}{2}\int_{{}}^{{}}{\text{cose}{{\text{c}}^{\text{2}}}t\,dt}\]                                                               \[=\frac{1}{2}\cot t=\frac{1}{2}\cot (2{{e}^{-x}}+5)+c\].


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