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Câu hỏi: Tất cả các nguyên hàm của hàm $f\left( x \right)=\dfrac{1}{\sqrt{3x-2}}$ là
A. $2\sqrt{3x-2}+C$.
B. $\dfrac{2}{3}\sqrt{3x-2}+C$.
C. $-\dfrac{2}{3}\sqrt{3x-2}+C$.
D. $-2\sqrt{3x-2}+C$.
Ta có $\int{\dfrac{1}{\sqrt{3x-2}}\text{d}x=\dfrac{1}{3}\int{{{\left( 3x-2 \right)}^{-\dfrac{1}{2}}}\text{d}\left( 3x-2 \right)=\dfrac{1}{3}.\dfrac{{{\left( 3x-2 \right)}^{\dfrac{1}{2}}}}{\dfrac{1}{2}}+C=\dfrac{2}{3}\sqrt{3x-2}+C.}}$
A. $2\sqrt{3x-2}+C$.
B. $\dfrac{2}{3}\sqrt{3x-2}+C$.
C. $-\dfrac{2}{3}\sqrt{3x-2}+C$.
D. $-2\sqrt{3x-2}+C$.
Ta có $\int{\dfrac{1}{\sqrt{3x-2}}\text{d}x=\dfrac{1}{3}\int{{{\left( 3x-2 \right)}^{-\dfrac{1}{2}}}\text{d}\left( 3x-2 \right)=\dfrac{1}{3}.\dfrac{{{\left( 3x-2 \right)}^{\dfrac{1}{2}}}}{\dfrac{1}{2}}+C=\dfrac{2}{3}\sqrt{3x-2}+C.}}$
Đáp án B.