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

  • question_answer
    \[\int_{{}}^{{}}{\tan (3x-5)\sec (3x-5)\ dx=}\]                    [MP PET 1988]

    A)            \[\sec (3x-5)+c\]

    B)            \[\frac{1}{3}\sec (3x-5)+c\]

    C)            \[\tan (3x-5)+c\]

    D)            None of these

    Correct Answer: B

    Solution :

                       Put \[t=3x-5\Rightarrow dt=3dx,\] therefore            \[\int_{{}}^{{}}{\tan (3x-5)\,\sec (3x-5)\,dx}=\frac{1}{3}\int_{{}}^{{}}{\tan t.\sec t\,dt}\]                                                               \[=\frac{\sec t}{3}+c=\frac{\sec (3x-5)}{3}+c.\]


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