Menu Close

Category: Integration

let-f-x-0-e-ax-ln-1-e-bx-dx-with-a-gt-0-and-b-gt-0-1-calculate-f-a-x-2-calculate-f-b-x-3-find-the-value-of-0-e-2x-ln-1-e-x-dx-and-0-e-x-ln-1-e-2x-

Question Number 41301 by math khazana by abdo last updated on 05/Aug/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{ax}} {ln}\left(\mathrm{1}+{e}^{−{bx}} \right){dx}\:{with}\:{a}>\mathrm{0}\:{and} \\ $$$${b}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\frac{\partial{f}}{\partial{a}}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\frac{\partial{f}}{\partial{b}}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}}…