Discuss-according-to-the-value-of-the-parametre-R-the-convergence-of-the-improper-integral-0-x-ln-x-e-x-dx-

Tinku Tara June 4, 2023 None 0 Comments

Question Number 186858 by aba last updated on 11/Feb/23

Discuss according to the value of the parametre α∈R the convergence of the improper integral ∫_0 ^(+∞) x^α ln(x+e^(αx) )dx

$${Discuss}\:{according}\:{to}\:{the}\:{value}\:{of}\:{the}\:{parametre} \\ $$$$\alpha\in\mathbb{R}\:{the}\:{convergence}\:{of}\:{the}\:{improper}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{+\infty} {x}^{\alpha} {ln}\left({x}+{e}^{\alpha{x}} \right){dx} \\ $$

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Discuss-according-to-the-value-of-the-parametre-R-the-convergence-of-the-improper-integral-0-x-ln-x-e-x-dx-

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