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Question Number 76424 by john santu last updated on 27/Dec/19

h o w t o c a l c u l a t e \int \sqrt{\frac{x}{\sqrt{\frac{x}{\sqrt{\frac{x}{\sqrt{\dots}}}}}}} d x ?

Commented by john santu last updated on 27/Dec/19

t h i s t h e c r a z y i n t e g r a t i o n

Answered by $@ty@m123 last updated on 27/Dec/19

y = \sqrt{\frac{x}{y}}

y^{2} = \frac{x}{y}

y^{3} = x

y = x^{\frac{1}{3}}

∴ t h e g i v e n i n t e g r a l

= \int x^{\frac{1}{3}} d x

= \frac{3}{4} x^{\frac{4}{3}} + C

Commented by john santu last updated on 27/Dec/19

t h a n k s y o u s i r