A Normal Distribution?

Calculus Level 4

Given that the indefinite integral

sin52xcos3x dx \large \int \sin^{\frac {5}{2}} x \cos^3 x \space \mathrm{d}x

equals to

2sinA2x[1B1Csin2x] \large 2 \sin^{ \frac {A}{2} } x \left [ \frac {1}{B} - \frac {1}{C} \sin^2 x \right ]

neglecting the arbitrary constant.

Find the value of A+BCA + B - C .


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