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