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Question Number 128279 by liberty last updated on 06/Jan/21

$$\mathrm{\Theta }={\int }_1^{\mathrm{e}}\frac{dx}{x.\sqrt[3]{\ln x}}?$$

Answered by john_santu last updated on 06/Jan/21

$$let\sqrt[3]{\ln x}=w\Rightarrow \frac{dx}{x}=3w^{2}dw$$$$\mathrm{\Theta }={\int }_0^1\frac{3w^2}{w}dw={\int }_0^{1}3wdw$$$$\mathrm{\Theta }=\frac{3}{2}{w}^2{\mid }_0^1=\frac{3}{2}.$$

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