# May not be substituted?

Calculus Level 5

$\large{\displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \ln (29+20\cos (2x)) \, dx =(A \pi^{B} \ln ( C) )^{D}}$

Given that the above equation is true for positive integers $$A,B,C$$ and $$D$$. Find $$A+B+C+D$$.

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