Google
Câu hỏi: Cho hàm số $f\left( x \right)=\sin x.{{\cos }^{3}}x$. Khẳng định nào dưới đây đúng?
A. $\int{f\left( x \right)\text{d}x=}\cos x+C$.
B. $\int{f\left( x \right)\text{d}x=}\dfrac{\text{co}{{\text{s}}^{4}}x}{4}+C$.
C. $\int{f\left( x \right)\text{d}x=}-\dfrac{\text{co}{{\text{s}}^{4}}x}{4}+C$.
D. $\int{f\left( x \right)\text{d}x=}\text{co}{{\text{s}}^{4}}x+C$.
A. $\int{f\left( x \right)\text{d}x=}\cos x+C$.
B. $\int{f\left( x \right)\text{d}x=}\dfrac{\text{co}{{\text{s}}^{4}}x}{4}+C$.
C. $\int{f\left( x \right)\text{d}x=}-\dfrac{\text{co}{{\text{s}}^{4}}x}{4}+C$.
D. $\int{f\left( x \right)\text{d}x=}\text{co}{{\text{s}}^{4}}x+C$.
Ta có : $\int{f\left( x \right)\text{d}x=}\int{\left( \sin x.{{\cos }^{3}}x \right)}\text{d}x=-\int{{{\cos }^{3}}x.}\text{d}\left( \cos x \right)=-\dfrac{{{\cos }^{4}}x}{4}+C$.
Đáp án C.