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