First slide

Methods of integration

Question

$\int x^{x} (1 + \log_{e} x) d x$ is equal to

Moderate

A

$x^{x} \log_{e} x + C$
B

$e^{x^{2}} + C$
C

$x^{x} + C$
D

none of these

Solution

We have,
$\int x^{x} (1 + \log_{e} x) d x = \int 1 \cdot d (x^{x}) = x^{x} + C$

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