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