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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 21

  • question_answer
    \[\int_{{}}^{{}}{{{e}^{x}}\left( \cos e{{c}^{-1}}x+\frac{-1}{x\sqrt{{{x}^{2}}-1}} \right)}dx\]is equal to

    A) \[{{e}^{x}}\cos e{{c}^{-1}}x+C\]

    B)        \[{{e}^{x}}{{\sin }^{-1}}x+C\]

    C) \[{{e}^{x}}{{\sec }^{-1}}x+C\]         

    D) \[{{e}^{x}}{{\cos }^{-1}}x+C\]

    Correct Answer: A

    Solution :

    [a] : Since \[\int_{{}}^{{}}{{{e}^{x}}(f(x)+f'(x))dx={{e}^{x}}f(x)+C}\] \[\therefore \]\[\int_{{}}^{{}}{{{e}^{x}}\left( \cos e{{c}^{-1}}x+\frac{(-1)}{x\sqrt{{{x}^{2}}-1}} \right)dx={{e}^{x}}\cos e{{c}^{-1}}x+C}\]


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