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Question Number 85360 by sahnaz last updated on 21/Mar/20

∫(e^((1−x)×e^x ) ×e^(∫xe^x dx) )dx

$$\int\left(\mathrm{e}^{\left(\mathrm{1}−\mathrm{x}\right)×\mathrm{e}^{\mathrm{x}} } ×\mathrm{e}^{\int\mathrm{xe}^{\mathrm{x}} \mathrm{dx}} \right)\mathrm{dx} \\ $$

Answered by john santu last updated on 21/Mar/20

∫ xe^x  dx = e^x  (x−1)   ∫ (e^((e^x −xe^x +xe^e −e^x ))  ) dx = ∫ e^0  dx = x+c

$$\int\:{xe}^{{x}} \:{dx}\:=\:{e}^{{x}} \:\left({x}−\mathrm{1}\right)\: \\ $$$$\int\:\left({e}^{\left({e}^{{x}} −{xe}^{{x}} +{xe}^{{e}} −{e}^{{x}} \right)} \:\right)\:{dx}\:=\:\int\:{e}^{\mathrm{0}} \:{dx}\:=\:{x}+{c} \\ $$

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