# Logarithms, Trignometry, Integrals (Part 3)

Calculus Level 5

$\large \int_0^{\pi /2} \ln \left( \left | \cos(\tan x ) \right | \right) \, dx$

The value of the integral above is equal to $\dfrac {A\pi }B \left( \ln\left( \dfrac{C+e^{-D}}F \right) \right)$

where $$A,B,C,D$$ and $$F$$ are positive integers with $$A,B$$ coprime and $$\displaystyle e = \lim_{n\to\infty} \left( 1 + \dfrac1n\right)^n \approx 2.71828$$.

Compute $$A+B+C+D+F$$.

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