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  4. ∫ xx (1 + log x)dx is equal to

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Q. $\int x^x (1 + \log \, x)dx$ is equal to

Integrals

Solution:

$I = \int \, x^x (1+ \log \, x)dx$
Put $x^x = t$, then $x^x ( 1 + logx) dx = dt$
$\therefore \, I = \int \, dt \, \Rightarrow \, I = t + C \, \Rightarrow \, I = x^x + C$.