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Q.
The value of the definite integral $\int_0^1 e ^{ e ^{ x }}\left(1+ x \cdot e ^{ x }\right) dx$ is equal to
Integrals
Solution:
Put $e ^{ x }= t \Rightarrow e ^{ x } dx = dt$
$x =\ln t$
$I=\int e^t \frac{(1+t \ln t)}{t} d t=\int e^t\left(\ln t+\frac{1}{t}\right) d t=\left.e^t \ln t\right|_1 ^e=e^e$