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Question Number 128276 by john_santu last updated on 06/Jan/21

$${\int }_{e^2}^{\mathrm{\infty }}\frac{dx}{x^3\ln x}?$$

Answered by liberty last updated on 06/Jan/21

$$ϝ=\underset{\mathrm{Y}\to +\mathrm{\infty }}{\lim }{\int }_{{\mathrm{e}}^2}^{\mathrm{Y}}\frac{dx}{x^3.\ln x}=\underset{\mathrm{Y}\to +\mathrm{\infty }}{\lim }{(-\frac{1}{2\ln {}^{2}x})}_{{\mathrm{e}}^2}^{\mathrm{Y}}$$$$ϝ=\underset{\mathrm{Y}\to +\mathrm{\infty }}{\lim }(\frac{1}{8}-\frac{1}{2\ln {}^2\mathrm{Y}})=\frac{1}{8}$$

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