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

  • question_answer
    \[\int_{{}}^{{}}{\frac{{{e}^{\sqrt{x}}}\cos {{e}^{\sqrt{x}}}}{\sqrt{x}}dx}=\]

    A)            \[2\sin {{e}^{\sqrt{x}}}\]

    B)            \[\sin {{e}^{\sqrt{x}}}\]

    C)            \[2\cos {{e}^{\sqrt{x}}}\]

    D)            \[-2\sin {{e}^{\sqrt{x}}}\]

    Correct Answer: A

    Solution :

               Put \[{{e}^{\sqrt{x}}}=t\Rightarrow \frac{{{e}^{\sqrt{x}}}}{\sqrt{x}}=\,2dt\], (Now proceed yourself).


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