The value of _0^1 e^ e^x ( 1 + x. e^x )dx is - Vidyadip

MCQ

The value of $\int\limits_0^1 {{e^{{e^x}}}} \left( {1 + x.{e^x}} \right)dx$ is

A
$e$
✓
$e^e$
C
$e^e -e$
D
$e^e -1$

✓

Answer

Correct option: B.

$e^e$

b
Put $\mathrm{e}^{\mathrm{x}}=\mathrm{t}$

$I = \int_1^e {{e^t}} \left( {\frac{{1 + t\ln t)}}{t}} \right)dt = \int_1^e {{e^t}} \left( {\ln t + \frac{1}{t}} \right)dt = {e^e}$

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