Google
Câu hỏi: Hàm số nào sau đây không phải là một nguyên hàm của hàm số $f\left( x \right)={{\left( 2x-3 \right)}^{3}}$ ?
A. $F\left( x \right)=\dfrac{{{\left( 2x-3 \right)}^{4}}}{8}+8$.
B. $F\left( x \right)=\dfrac{{{\left( 2x-3 \right)}^{4}}}{8}-3$.
C. $F\left( x \right)=\dfrac{{{\left( 2x-3 \right)}^{4}}}{8}$.
D. $F\left( x \right)=\dfrac{{{\left( 2x-3 \right)}^{4}}}{4}$.
Ta có $f\left( x \right)={{\left( 2x-3 \right)}^{3}}\Rightarrow \int{f\left( x \right)\text{d}x=\int{{{\left( 2x-3 \right)}^{3}}\text{d}x=\dfrac{1}{2}}}\dfrac{{{\left( 2x-3 \right)}^{4}}}{4}+C=\dfrac{{{\left( 2x-3 \right)}^{4}}}{8}+C$.
A. $F\left( x \right)=\dfrac{{{\left( 2x-3 \right)}^{4}}}{8}+8$.
B. $F\left( x \right)=\dfrac{{{\left( 2x-3 \right)}^{4}}}{8}-3$.
C. $F\left( x \right)=\dfrac{{{\left( 2x-3 \right)}^{4}}}{8}$.
D. $F\left( x \right)=\dfrac{{{\left( 2x-3 \right)}^{4}}}{4}$.
Ta có $f\left( x \right)={{\left( 2x-3 \right)}^{3}}\Rightarrow \int{f\left( x \right)\text{d}x=\int{{{\left( 2x-3 \right)}^{3}}\text{d}x=\dfrac{1}{2}}}\dfrac{{{\left( 2x-3 \right)}^{4}}}{4}+C=\dfrac{{{\left( 2x-3 \right)}^{4}}}{8}+C$.
Đáp án D.