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Question-201646




Question Number 201646 by Calculusboy last updated on 10/Dec/23
Answered by aleks041103 last updated on 10/Dec/23
(x)^(1/(ln(x))) =x^(1/(ln(x))) =(e^(ln(x)) )^(1/(ln(x))) =e=const  ⇒∫(x)^(1/(ln(x)))  dx = ex + C
$$\sqrt[{{ln}\left({x}\right)}]{{x}}={x}^{\frac{\mathrm{1}}{{ln}\left({x}\right)}} =\left({e}^{{ln}\left({x}\right)} \right)^{\frac{\mathrm{1}}{{ln}\left({x}\right)}} ={e}={const} \\ $$$$\Rightarrow\int\sqrt[{{ln}\left({x}\right)}]{{x}}\:{dx}\:=\:{ex}\:+\:{C} \\ $$

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