1 x^3 [ x^x ]^2 d x= p ( x )^3+ c , then p =_____ - Vidyadip

Question

$\int \frac{1}{x^3}\left[\log x^x\right]^2 d x= p (\log x )^3+ c \text {, then } p =$_____

✓

Answer

$\frac{1}{3}$
Hint:
$\frac{1}{x^3}\left(\log x^x\right)^2=\frac{1}{x^3}(x \log x)^2=\frac{(\log x)^2}{x}$

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