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Câu hỏi: Trên khoảng $\left( 0;+\infty \right)$, họ nguyên hàm của hàm số $f\left( x \right)={{x}^{\dfrac{4}{3}}}$ là
A. $\int{f\left( x \right)\text{d}x}=\dfrac{3}{4}{{x}^{\dfrac{1}{3}}}+C\cdot $
B. $\int{f\left( x \right)\text{d}x}=\dfrac{4}{3}{{x}^{\dfrac{1}{3}}}+C\cdot $
C. $\int{f\left( x \right)\text{d}x}=\dfrac{7}{3}{{x}^{\dfrac{7}{3}}}+C\cdot $
D. $\int{f\left( x \right)\text{d}x}=\dfrac{3}{7}{{x}^{\dfrac{7}{3}}}+C\cdot $
A. $\int{f\left( x \right)\text{d}x}=\dfrac{3}{4}{{x}^{\dfrac{1}{3}}}+C\cdot $
B. $\int{f\left( x \right)\text{d}x}=\dfrac{4}{3}{{x}^{\dfrac{1}{3}}}+C\cdot $
C. $\int{f\left( x \right)\text{d}x}=\dfrac{7}{3}{{x}^{\dfrac{7}{3}}}+C\cdot $
D. $\int{f\left( x \right)\text{d}x}=\dfrac{3}{7}{{x}^{\dfrac{7}{3}}}+C\cdot $
Ta có $\int{f\left( x \right)\text{d}x}=\int{{{x}^{\dfrac{4}{3}}} \text{d}x}=\dfrac{{{x}^{\dfrac{4}{3}+1}}}{^{\dfrac{4}{3}+1}}+C=\dfrac{{{x}^{\dfrac{7}{3}}}}{\dfrac{7}{3}}+C=\dfrac{3}{7}{{x}^{\dfrac{7}{3}}}+C\cdot $
Đáp án D.