Câu hỏi 17

\(\begin{array}{l}\int\limits_{}^{} {f\left( x \right)dx}  = \int\limits_{}^{} {2x\left( {\sin x + 1} \right)dx}  = 2\int\limits_{}^{} {x\sin xdx}  + \int\limits_{}^{} {2xdx}  = 2{I_1} + {I_2}\\{I_2} = \int\limits_{}^{} {2xdx}  = {x^2} + {C_2}\\{I_1} = \int\limits_{}^{} {x\sin xdx}  =  - \int\limits_{}^{} {xd\left( {\cos x} \right)}  =  - \left[ {x\cos x - \int\limits_{}^{} {\cos xdx}  + {C_1}} \right]\\\,\,\,\,\,\, =  - x\cos x + \sin x + {C_1}\\ \Rightarrow \int\limits_{}^{} {f\left( x \right)dx}  =  - 2x\cos x + 2\sin x + {x^2} + C\end{array}\)

Chọn A.