Mathematics

Solve :
$$ \int e^x e^{e^x} e^{e^{e^x}} dx $$


SOLUTION
Given 
$$\int{e^xe^{e^x}e^{e^{e^x}}}dx$$

$$=\int{e^{e^{e^x}+e^x+x}}dx$$

Substitute $$u=e^x$$    $$dx=e^{-x}du$$

$$=\int{e^{e^u+u}}du$$

Substitute $$v=e^u$$    $$du=e^{-u}dv$$

$$=\int{e^v}dv$$

$$=e^v$$

$$=e^{e^u}$$

$$=e^{e^{e^x}}+c$$
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Subjective Medium Published on 17th 09, 2020
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