If-f-x-x-2-3-x-2-3-find-f-x-dx-

Question Number 18232 by Joel577 last updated on 17/Jul/17

If f (x) = \sqrt{x^{2} \sqrt{3 \sqrt{x^{2} \sqrt{3 \sqrt{} \dots}}}}

find \int f (x) d x

Answered by alex041103 last updated on 17/Jul/17

f (x) = \sqrt{x^{2} \sqrt{3 f (x)}}

\Rightarrow f^{4} (x) = 3 x^{4} f (x)

f^{3} (x) = 3 x^{4} \Rightarrow f (x) = \sqrt[3]{3} \times x^{4 / 3}

\int f (x) d x = \sqrt[3]{3} \int x^{4 / 3} d x = \sqrt[3]{3} \times \frac{3}{7} x^{7 / 3} + C

Commented by Joel577 last updated on 17/Jul/17

t h a n k y o u v e r y m u c h

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