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Câu hỏi: Khẳng định nào sau đây đúng?
A. $\int{x{{\left( {{x}^{2}}+7 \right)}^{15}}\text{d}x=\dfrac{1}{32}{{\left( {{x}^{2}}+7\right)}^{16}}+C}$.
B. $\int{x{{\left( {{x}^{2}}+7 \right)}^{15}}\text{d}x=\dfrac{1}{32}{{\left( {{x}^{2}}+7 \right)}^{16}}}$.
C. $\int{x{{\left( {{x}^{2}}+7 \right)}^{15}}\text{d}x=\dfrac{1}{16}{{\left( {{x}^{2}}+7 \right)}^{16}}}$.
D. $\int{x{{\left( {{x}^{2}}+7 \right)}^{15}}\text{d}x=\dfrac{1}{2}{{\left( {{x}^{2}}+7 \right)}^{16}}+C}$.
A. $\int{x{{\left( {{x}^{2}}+7 \right)}^{15}}\text{d}x=\dfrac{1}{32}{{\left( {{x}^{2}}+7\right)}^{16}}+C}$.
B. $\int{x{{\left( {{x}^{2}}+7 \right)}^{15}}\text{d}x=\dfrac{1}{32}{{\left( {{x}^{2}}+7 \right)}^{16}}}$.
C. $\int{x{{\left( {{x}^{2}}+7 \right)}^{15}}\text{d}x=\dfrac{1}{16}{{\left( {{x}^{2}}+7 \right)}^{16}}}$.
D. $\int{x{{\left( {{x}^{2}}+7 \right)}^{15}}\text{d}x=\dfrac{1}{2}{{\left( {{x}^{2}}+7 \right)}^{16}}+C}$.
Đặt $t={{x}^{2}}+7\Rightarrow \text{d}t=2x\text{d}x$.
Khi đó: $\int{x{{\left( {{x}^{2}}+7 \right)}^{15}}\text{d}x=}\dfrac{1}{2}\int{{{t}^{15}}\text{d}t=\dfrac{1}{32}}{{t}^{16}}+C=\dfrac{1}{32}{{\left( {{x}^{2}}+7 \right)}^{16}}+C$
Khi đó: $\int{x{{\left( {{x}^{2}}+7 \right)}^{15}}\text{d}x=}\dfrac{1}{2}\int{{{t}^{15}}\text{d}t=\dfrac{1}{32}}{{t}^{16}}+C=\dfrac{1}{32}{{\left( {{x}^{2}}+7 \right)}^{16}}+C$
Đáp án A.