# When integrals meet abominable numbers

Calculus Level 5

$\int_0^{\frac \pi 2 } \bigg [ ( \sin^{12} x ) \ln (\sin x) \bigg ] \ dx = \frac {\pi}{A \cdot 2^B} \ (C - D \ln 2)$

The equation above is true for integer constants $$A,B,C,D$$. Find sum of the sum of digits of $$A,B,C$$ and $$D$$

Hints:

$$A$$, $$B$$ are $$2$$-digit numbers which differ by $$1$$. $$C$$ and $$D$$ are 5 digit numbers of which $$C$$ has only two prime factors.