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Câu hỏi: Tìm nguyên hàm của hàm số $f\left( x \right)=\dfrac{x}{\sqrt{3{{\text{x}}^{2}}+2}}$.
A. $\dfrac{1}{3}\sqrt{3{{\text{x}}^{2}}+2}+C$
B. $C-\dfrac{1}{3}\sqrt{3{{\text{x}}^{2}}+2}$
C. $\dfrac{1}{6}\sqrt{3{{\text{x}}^{2}}+2}+C$
D. $\dfrac{2\sqrt{3{{\text{x}}^{2}}+2}}{3}+C$
A. $\dfrac{1}{3}\sqrt{3{{\text{x}}^{2}}+2}+C$
B. $C-\dfrac{1}{3}\sqrt{3{{\text{x}}^{2}}+2}$
C. $\dfrac{1}{6}\sqrt{3{{\text{x}}^{2}}+2}+C$
D. $\dfrac{2\sqrt{3{{\text{x}}^{2}}+2}}{3}+C$
$\int{\dfrac{x}{\sqrt{3{{x}^{2}}+2}}dx}=\dfrac{1}{6}\int{\dfrac{d\left( 3{{x}^{2}}+2 \right)}{\sqrt{3{{x}^{2}}+2}}}=\dfrac{1}{3}\sqrt{3{{x}^{2}}+2}+C$.
Đáp án A.