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Question Number 143755 by Ar Brandon last updated on 18/Jun/21

$$\mathrm{Study}\mathrm{the}\mathrm{convergence}\mathrm{with}\mathrm{respect}\mathrm{to}$$$$\alpha \mathrm{and}\beta \mathrm{the}\mathrm{improper}\mathrm{integral}\mathrm{below};$$$${\int }_0^{\mathrm{\infty }}\frac{\mathrm{dx}}{{\mathrm{x}}^{\alpha }{\left(\mathrm{lnx}\right)}^{\beta }}$$

Answered by mathmax by abdo last updated on 18/Jun/21

$$\mathrm{a}\mathrm{lots}\mathrm{of}\mathrm{case}\mathrm{see}\mathrm{bertrand}\mathrm{integral}...$$

Commented by Ar Brandon last updated on 18/Jun/21

$${\mathrm{I}}^{\prime }\mathrm{m}\mathrm{aware}{\mathrm{it}}^{\prime }\mathrm{s}{\mathrm{Bertrand}}^{\prime }\mathrm{s}\mathrm{integral}.\mathrm{But}{\mathrm{can}}^{\prime }\mathrm{t}\mathrm{find}$$$$\mathrm{any}\mathrm{reliable}\mathrm{link}.\mathrm{Can}\mathrm{you}\mathrm{recommend}\mathrm{me}\mathrm{one}?$$

Commented by mathmax by abdo last updated on 20/Jun/21

$$\mathrm{take}\mathrm{a}\mathrm{look}\mathrm{at}\mathrm{google}...$$

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