A common integral in disguise

Calculus Level 3

∫0π/2ln⁡(cos⁡(x)) dx\large \int_0^{\pi/2}\ln(\cos(x))\, dx

If the above integral can be expressed as −πalog⁡(z)-\frac{\pi}{a} \log (z) for positive integers a,za,z, find a+za+z.

Siddharth Bhatt by siddharth bhatt
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