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Câu hỏi: Cho hàm số $f\left( x \right)={{2}^{x}}+x+1$. Tìm $\int{f\left( x \right)\text{d}x}$
A. $\int{f\left( x \right)\text{d}x}={{2}^{x}}+{{x}^{2}}+x+C$.
B. $\int{f\left( x \right)\text{d}x}=\dfrac{1}{\ln 2}{{2}^{x}}+\dfrac{1}{2}{{x}^{2}}+x+C$.
C. $\int{f\left( x \right)\text{d}x}={{2}^{x}}+\dfrac{1}{2}{{x}^{2}}+x+C$.
D. $\int{f\left( x \right)\text{d}x}=\dfrac{1}{x+1}{{2}^{x}}+\dfrac{1}{2}{{x}^{2}}+x+C$.
A. $\int{f\left( x \right)\text{d}x}={{2}^{x}}+{{x}^{2}}+x+C$.
B. $\int{f\left( x \right)\text{d}x}=\dfrac{1}{\ln 2}{{2}^{x}}+\dfrac{1}{2}{{x}^{2}}+x+C$.
C. $\int{f\left( x \right)\text{d}x}={{2}^{x}}+\dfrac{1}{2}{{x}^{2}}+x+C$.
D. $\int{f\left( x \right)\text{d}x}=\dfrac{1}{x+1}{{2}^{x}}+\dfrac{1}{2}{{x}^{2}}+x+C$.
Ta có: $\int{\left( {{2}^{x}}+x+1 \right)\text{d}x}=\dfrac{1}{\ln 2}{{2}^{x}}+\dfrac{1}{2}{{x}^{2}}+x+C$.
Đáp án B.