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Câu hỏi: $I=\int{x\operatorname{cosxdx}}$ bằng:
A. $\dfrac{{{x}^{2}}}{2}\operatorname{s}\text{inx+C}$
B. $x\sin x+\cos x+C$
C. $x\sin x-\sin x+C$
D. $\dfrac{{{x}^{2}}}{2}\cos x+C$
A. $\dfrac{{{x}^{2}}}{2}\operatorname{s}\text{inx+C}$
B. $x\sin x+\cos x+C$
C. $x\sin x-\sin x+C$
D. $\dfrac{{{x}^{2}}}{2}\cos x+C$
Đặt $\left\{ \begin{aligned}
& x=u\Rightarrow dx=du \\
& \operatorname{cosxdx}=dv\Rightarrow v=sinx \\
\end{aligned} \right. $ ta có: $ I=\int{x\cos xdx}=x\sin x-\int{x\sin xdx}=x\sin x+\cos x+C$
& x=u\Rightarrow dx=du \\
& \operatorname{cosxdx}=dv\Rightarrow v=sinx \\
\end{aligned} \right. $ ta có: $ I=\int{x\cos xdx}=x\sin x-\int{x\sin xdx}=x\sin x+\cos x+C$
Đáp án B.