Google
Câu hỏi: Trong các mệnh đề sau mệnh đề nào sai?
A. $\int{\tan xdx=-\ln \left| \cos x \right|+C.}$
B. $\int{\cot xdx=\ln \left| \sin x \right|+C.}$
C. $\int{\dfrac{dx}{\sin x}=\dfrac{1}{2}\ln \left| \dfrac{\cos x-1}{\cos x+1} \right|+C.}$
D. $\int{\dfrac{dx}{\cos x}=\dfrac{1}{2}\ln \left| \dfrac{\sin x-1}{\sin x+1} \right|}+C.$
A. $\int{\tan xdx=-\ln \left| \cos x \right|+C.}$
B. $\int{\cot xdx=\ln \left| \sin x \right|+C.}$
C. $\int{\dfrac{dx}{\sin x}=\dfrac{1}{2}\ln \left| \dfrac{\cos x-1}{\cos x+1} \right|+C.}$
D. $\int{\dfrac{dx}{\cos x}=\dfrac{1}{2}\ln \left| \dfrac{\sin x-1}{\sin x+1} \right|}+C.$
Ta có $\int{\dfrac{dx}{\cos x}=\int{\dfrac{\cos x}{{{\cos }^{2}}x}dx}=\int{\dfrac{1}{1-{{\sin }^{2}}x}d\left( \sin x \right)}=-\dfrac{1}{2}\int{\left( \dfrac{1}{\sin x-1}-\dfrac{1}{\sin x+1} \right)d\left( \sin x \right)}}$
$=-\dfrac{1}{2}\ln \left| \dfrac{\sin x-1}{\sin x+1} \right|+C.$
$=-\dfrac{1}{2}\ln \left| \dfrac{\sin x-1}{\sin x+1} \right|+C.$
Đáp án D.