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Câu hỏi: Tìm nguyên hàm $\int{x{{\left( {{x}^{2}}+7 \right)}^{9}}\text{d}x}$ ?
A. $\dfrac{1}{20}{{({{x}^{2}}+7)}^{10}}+C$.
B. $9{{({{x}^{2}}+7)}^{8}}+C$.
C. $\dfrac{1}{16}{{({{x}^{2}}+7)}^{8}}+C$.
D. $\dfrac{1}{10}{{\left( {{x}^{2}}+7 \right)}^{10}}+C$.
A. $\dfrac{1}{20}{{({{x}^{2}}+7)}^{10}}+C$.
B. $9{{({{x}^{2}}+7)}^{8}}+C$.
C. $\dfrac{1}{16}{{({{x}^{2}}+7)}^{8}}+C$.
D. $\dfrac{1}{10}{{\left( {{x}^{2}}+7 \right)}^{10}}+C$.
Ta có $\int{x{{\left( {{x}^{2}}+7 \right)}^{9}}\text{d}x}=\dfrac{1}{2}\int{{{\left( {{x}^{2}}+7 \right)}^{9}}\text{d(}{{x}^{2}}+7)}=\dfrac{1}{20}{{\left( {{x}^{2}}+7 \right)}^{10}}+C$
Đáp án A.