# Logarithm raised to what?

Calculus Level 5

$\large \int_0^{\pi/2} ( \ln (\cos x))^2 ( (\ln(\cos x))^2 - 6x^2) \, dx$

If the integral above is equal to $$\dfrac{\pi^a}2 (\ln 2)^b - \dfrac{\pi^c}d$$, where $$a,b,c$$ and $$d$$ are positive integers, find $$a+b+c+d$$.

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