Integrate with sin cos
Calculus
Level
5
\[\large\displaystyle \int_{0}^{\frac{\pi}{4}} (\cos 2 \theta)^{\frac{3}{2}} \cos \theta \, d \theta\]
Given the integral above equals to \( \dfrac{A}{B \sqrt{C}} \pi\) where \(A,B,C\) are positive integers with \(A,B\) are coprime and \(C\) square-free. Find \(B-A-C\).
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Tanishq Varshney