_1^e ( (x + 1 ). e^x x )dx , = - Vidyadip

MCQ

$\int\limits_1^e {\left( {(x + 1} \right).{e^x}\ln x} )dx\, = $

A
$e$
B
$e^e+1$
C
$e^e(e-1)$
✓
$e^e(e-1)+e$

✓

Answer

Correct option: D.

$e^e(e-1)+e$

d
$\int e^{x}(f(x))+f^{\prime}(x) d x=e^{x} f(x)$

$\int {{e^x}} (x\ln x - 1 + 1 + \ln x) = {e^x}(x\ln x - 1)$

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