Tìm nguyên hàm \(I = \int {\left( {x - 1} \right)\sin 2xdx} .\)

Tìm nguyên hàm \(I = \int {\left( {x - 1} \right)\sin 2xdx} .\)
A. \(I = \frac{{\left( {1 - 2x} \right)\cos 2x + \sin 2x}}{2} + C\)
B. \(I = \frac{{\left( {2 - 2x} \right)\cos 2x + \sin 2x}}{2} + C\)
C. \(I = \frac{{\left( {1 - 2x} \right)\cos 2x + \sin 2x}}{4} + C\)
D. \(I = \frac{{\left( {2- 2x} \right)\cos 2x + \sin 2x}}{24} + C\)

Đặt: \(\left\{ \begin{array}{l} u = x - 1\\ dv = \sin 2xdx \end{array} \right. \Rightarrow \left\{ \begin{array}{l} du = dx\\ v = - \frac{1}{2}\cos 2x \end{array} \right.\)
\(\begin{array}{l} \int {\left( {x - 1} \right)\sin 2xdx} = - \left( {x - 1} \right)\frac{1}{2}\cos 2x + \int {\frac{1}{2}\cos 2xdx} \\ = - \left( {x - 1} \right)\frac{1}{2}\cos 2x + \frac{1}{4}\sin 2x + C \end{array}\)