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Câu hỏi: Hàm số nào dưới đây không là nguyên hàm của hàm số $f(x)=\sin ^2 x$ ?
A. $F(x)=\dfrac{1}{2}\left(x-\dfrac{\sin 2 x}{2}\right)+C$.
B. $F(x)=\dfrac{1}{4}(2 x-\sin x \cos x)+C$
C. $F(x)=\dfrac{1}{2}(x-\sin x \cos x)+C$.
D. $F(x)=\dfrac{1}{4}(2 x-\sin 2 x)+C$.
A. $F(x)=\dfrac{1}{2}\left(x-\dfrac{\sin 2 x}{2}\right)+C$.
B. $F(x)=\dfrac{1}{4}(2 x-\sin x \cos x)+C$
C. $F(x)=\dfrac{1}{2}(x-\sin x \cos x)+C$.
D. $F(x)=\dfrac{1}{4}(2 x-\sin 2 x)+C$.
$
\begin{aligned}
& \int \sin ^2 x \mathrm{~d} x=\int \dfrac{1}{2} \mathrm{~d} x-\int \dfrac{1}{2} \cos 2 x \mathrm{~d} x=\dfrac{1}{2} x-\dfrac{1}{4} \sin 2 x+C=\dfrac{1}{2}(x-\sin x \cos x)+C=\dfrac{1}{2}\left(x-\dfrac{\sin 2 x}{2}\right)+ \\& C=\dfrac{1}{4}(2 x-\sin 2 x)+C .
\end{aligned}
$
\begin{aligned}
& \int \sin ^2 x \mathrm{~d} x=\int \dfrac{1}{2} \mathrm{~d} x-\int \dfrac{1}{2} \cos 2 x \mathrm{~d} x=\dfrac{1}{2} x-\dfrac{1}{4} \sin 2 x+C=\dfrac{1}{2}(x-\sin x \cos x)+C=\dfrac{1}{2}\left(x-\dfrac{\sin 2 x}{2}\right)+ \\& C=\dfrac{1}{4}(2 x-\sin 2 x)+C .
\end{aligned}
$
Đáp án D.