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Câu hỏi: Cho hàm số $f\left( x \right)=1-\dfrac{1}{{{\cos }^{2}}2x}$. Khẳng định nào dưới đây đúng?
A. $\int{f\left( x \right)\text{d}x=x+\tan 2x+C}$.
B. $\int{f\left( x \right)\text{d}x=x+\dfrac{1}{2}\cot 2x+C}$.
C. $\int{f\left( x \right)\text{d}x=x-\dfrac{1}{2}\tan 2x+C}$.
D. $\int{f\left( x \right)\text{d}x=x+\dfrac{1}{2}\tan 2x+C}$.
A. $\int{f\left( x \right)\text{d}x=x+\tan 2x+C}$.
B. $\int{f\left( x \right)\text{d}x=x+\dfrac{1}{2}\cot 2x+C}$.
C. $\int{f\left( x \right)\text{d}x=x-\dfrac{1}{2}\tan 2x+C}$.
D. $\int{f\left( x \right)\text{d}x=x+\dfrac{1}{2}\tan 2x+C}$.
Ta có, $\int{f\left( x \right)\text{d}x=\int{\left( 1-\dfrac{1}{{{\cos }^{2}}2x} \right)\text{d}x=\int{1\text{d}x-\int{\dfrac{1}{{{\cos }^{2}}2x}\text{d}x=x-\dfrac{1}{2}\tan 2x+C}}}}$.
Đáp án C.