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Câu hỏi: Cho hàm số $f\left( x \right)=x.{{\left( {{x}^{2}}+1 \right)}^{2016}}$. Khi đó:
A. $\int{f\left( x \right)}d\text{x}=\dfrac{{{\left( {{x}^{2}}+1 \right)}^{2017}}}{2017}+C.$
B. $\int{f\left( x \right)}d\text{x}=\dfrac{{{\left( {{x}^{2}}+1 \right)}^{2016}}}{2016}+C.$
C. $\int{f\left( x \right)}d\text{x}=\dfrac{{{\left( {{x}^{2}}+1 \right)}^{2017}}}{4034}+C.$
D. $\int{f\left( x \right)}d\text{x}=\dfrac{{{\left( {{x}^{2}}+1 \right)}^{2016}}}{4032}+C.$
A. $\int{f\left( x \right)}d\text{x}=\dfrac{{{\left( {{x}^{2}}+1 \right)}^{2017}}}{2017}+C.$
B. $\int{f\left( x \right)}d\text{x}=\dfrac{{{\left( {{x}^{2}}+1 \right)}^{2016}}}{2016}+C.$
C. $\int{f\left( x \right)}d\text{x}=\dfrac{{{\left( {{x}^{2}}+1 \right)}^{2017}}}{4034}+C.$
D. $\int{f\left( x \right)}d\text{x}=\dfrac{{{\left( {{x}^{2}}+1 \right)}^{2016}}}{4032}+C.$
$\int{f\left( x \right)}d\text{x}=\int{x.{{\left( {{x}^{2}}+1 \right)}^{2016}}d\text{x}=\dfrac{1}{2}\int{{{\left( {{x}^{2}}+1 \right)}^{2016}}.d\left( {{x}^{2}}+1 \right)}}=\dfrac{{{\left( {{x}^{2}}+1 \right)}^{2017}}}{4034}+C.$
Đáp án C.