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Câu hỏi: Trong các mệnh đề sau, mệnh đề nào sai?
A. $\int{{f}'\left( x \right)\text{d}x=f\left( x \right)+C}$.
B. $\int{\cos x\text{d}x=\sin x+C}$.
C. $\int{{{x}^{\alpha }}\text{d}x=\dfrac{{{x}^{\alpha +1}}}{\alpha +1}+C},\forall \alpha \ne -1$.
D. $\int{{{a}^{x}}}\text{d}x={{a}^{x}}\ln a+C$ $\left( 0<a\ne 1 \right)$.
A. $\int{{f}'\left( x \right)\text{d}x=f\left( x \right)+C}$.
B. $\int{\cos x\text{d}x=\sin x+C}$.
C. $\int{{{x}^{\alpha }}\text{d}x=\dfrac{{{x}^{\alpha +1}}}{\alpha +1}+C},\forall \alpha \ne -1$.
D. $\int{{{a}^{x}}}\text{d}x={{a}^{x}}\ln a+C$ $\left( 0<a\ne 1 \right)$.
Ta có $\int{{{a}^{x}}}\text{d}x=\dfrac{{{a}^{x}}}{\ln a}+C$ $\left( 0<a\ne 1 \right)$ nên phương án $\int{{{a}^{x}}}\text{d}x={{a}^{x}}\ln a+C$ $\left( 0<a\ne 1 \right)$ sai.Đáp án D.