First slide

Methods of integration

Question

$\int x^{x} (1 + \log | x |) dx$ is equal to

Easy

A

$x^{x} \log | x | + C$
B

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

$x^{x} + C$
D

None of these

Solution

put $x^{x} = t \Rightarrow x^{x} (1 + \log_{e} | x |) dx = dt$
$\int x^{x} (1 + \log_{e} ∣ x!) dx = t + C = x^{x} + C$

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