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Câu hỏi: Biết $\int{f\left( u \right)du=F\left( u \right)+C}$. Mệnh đề nào dưới đây đúng?
A. $\int{f\left( 2x-1 \right)dx}=2F\left( 2x-1 \right)+C$.
B. $\int{f\left( 2x-1 \right)dx}=2F\left( x \right)-1+C$.
C. $\int{f\left( 2x-1 \right)dx}=F\left( 2x-1 \right)+C$.
D. $\int{f\left( 2x-1 \right)dx}=\dfrac{1}{2}F\left( 2x-1 \right)+C$.
A. $\int{f\left( 2x-1 \right)dx}=2F\left( 2x-1 \right)+C$.
B. $\int{f\left( 2x-1 \right)dx}=2F\left( x \right)-1+C$.
C. $\int{f\left( 2x-1 \right)dx}=F\left( 2x-1 \right)+C$.
D. $\int{f\left( 2x-1 \right)dx}=\dfrac{1}{2}F\left( 2x-1 \right)+C$.
Đặt $u=2x-1\Rightarrow du=2dx$
$\int{f\left( 2x-1 \right)dx}=\int{\dfrac{f\left( u \right)du}{2}}=\dfrac{1}{2}F\left( u \right)+C=\dfrac{1}{2}F\left( 2x-1 \right)+C.$
$\int{f\left( 2x-1 \right)dx}=\int{\dfrac{f\left( u \right)du}{2}}=\dfrac{1}{2}F\left( u \right)+C=\dfrac{1}{2}F\left( 2x-1 \right)+C.$
Đáp án D.