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e-x-e-x-dx-




Question Number 132612 by aurpeyz last updated on 15/Feb/21
∫e^(x+e^x ) dx
$$\int{e}^{{x}+{e}^{{x}} } {dx} \\ $$
Answered by Dwaipayan Shikari last updated on 15/Feb/21
∫e^x e^e^x  dx              e^x =t  =∫e^t dt=e^t +C=e^e^x  +C
$$\int{e}^{{x}} {e}^{{e}^{{x}} } {dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:{e}^{{x}} ={t} \\ $$$$=\int{e}^{{t}} {dt}={e}^{{t}} +{C}={e}^{{e}^{{x}} } +{C} \\ $$

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