Tìm nguyên hàm:

Câu hỏi: Tìm nguyên hàm: $I=\int \frac{{\sin }^{4}2x.co{s}^{3}x}{\tan \left(x+{\displaystyle \frac{\mathrm{\pi }}{4}}\right)\tan \left(x-\frac{\mathrm{\pi }}{4}\right)}dx$.

A. $16\left(\frac{{\sin }^{11}x}{11}-\frac{{\sin }^{9}x}{3}+\frac{3{\sin }^{7}x}{7}-\frac{{\sin }^{5}x}{5}+C\right)$

B. $16\left(\frac{{\sin }^{11}x}{11}+\frac{{\sin }^{9}x}{3}+\frac{{\sin }^{7}x}{7}-\frac{{\sin }^{5}x}{5}+C\right)$

C. $16\left(\frac{{\sin }^{11}x}{11}-\frac{{\sin }^{9}x}{3}+\frac{{\sin }^{7}x}{7}+\frac{{\sin }^{5}x}{5}+C\right)$

D. Tất cả đều sai