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KVPY Sample Paper KVPY Stream-SX Model Paper-27

  • question_answer
    \[\int{\frac{x\,\,dx}{\sqrt{1+{{x}^{2}}+\sqrt{{{(1+{{x}^{2}})}^{3}}}}}}\]is equal to -

    A) \[\frac{1}{2}\ell n\,\,(1+\sqrt{1+{{x}^{2}})}+c\]

    B) \[2\sqrt{1+\sqrt{1+{{x}^{2}}}}+c\]

    C) \[2\,\,(1+\sqrt{1+{{x}^{2}}})+c\]

    D) None of these

    Correct Answer: B

    Solution :

    \[\frac{x}{\sqrt{(1+{{x}^{2}})\left( 1+\sqrt{1+{{x}^{2}}} \right)}};\] put \[1+\sqrt{1+{{x}^{2}}}={{t}^{2}}]\]


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