Question

Evaluate the following integrals :
$\displaystyle \sf \int \sqrt{x} \: tan \bigg \{2 {tan}^{ - 1} \bigg( \dfrac{ \sqrt{ \sqrt{1 + \sqrt{x}} + 1} \: - \sqrt{ \sqrt{1 + \sqrt{x} } - 1 } }{ \sqrt{ \sqrt{1 + \sqrt{x}} + 1} \: + \sqrt{ \sqrt{1 + \sqrt{x} } - 1 }} \bigg) \bigg \} \: dx∫x​tan{2tan−1(1+x​​+1​+1+x​​−1​1+x​​+1​−1+x​​−1​​)}dx$
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Answer 1

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Answer 2

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