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Câu hỏi: Trên khoảng $\left( 0,+\infty \right)$, họ nguyên hàm của hàm số $f(x)={{x}^{\dfrac{5}{2}}}$ là:
A. ${\displaystyle\int f(x) \mathrm{d} x=\dfrac{3}{2} x^{\dfrac{1}{2}}+C}$.
B. ${\displaystyle\int f(x) \mathrm{d} x=\dfrac{3}{2} x^{\dfrac{1}{2}}+C}$.
C. ${\displaystyle\int f(x) \mathrm{d} x=\dfrac{3}{2} x^{\dfrac{1}{2}}+C}$.
D. ${\displaystyle\int f(x) \mathrm{d} x=\dfrac{3}{2} x^{\dfrac{1}{2}}+C}$.
A. ${\displaystyle\int f(x) \mathrm{d} x=\dfrac{3}{2} x^{\dfrac{1}{2}}+C}$.
B. ${\displaystyle\int f(x) \mathrm{d} x=\dfrac{3}{2} x^{\dfrac{1}{2}}+C}$.
C. ${\displaystyle\int f(x) \mathrm{d} x=\dfrac{3}{2} x^{\dfrac{1}{2}}+C}$.
D. ${\displaystyle\int f(x) \mathrm{d} x=\dfrac{3}{2} x^{\dfrac{1}{2}}+C}$.
Ta có: $\int{{{x}^{\dfrac{5}{2}}}}\text{d}x=\dfrac{1}{\dfrac{5}{2}+1}{{x}^{\dfrac{5}{2}+1}}+C=\dfrac{2}{7}{{x}^{\dfrac{7}{2}}}+C$
Đáp án A.