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