Đáp án:
$F(x)=-\dfrac{2}{3}\cos ^3x+1$
Giải thích các bước giải:
$\int \sin 2x\cos xdx$
$=\int 2\sin x.\cos x\cos xdx$
$=\int 2\cos^2x .\sin xdx$
$=\int -2\cos^2x d\cos x$
$=-\dfrac{2}{3}\cos ^3x+C$
$\rightarrow F(x)=-\dfrac{2}{3}\cos ^3x+C$
Mà $F(0)=\dfrac{1}{3}\rightarrow -\dfrac{2}{3}\cos ^30+C=\dfrac{1}{3}\rightarrow C=1$
$\rightarrow F(x)=-\dfrac{2}{3}\cos ^3x+1$