Tính $I=\int\limits_{0}^{\frac{\pi }{3}}{\left( {{\tan }^{2}}x+x \right)\sin xdx}$

$I=\displaystyle\int\limits_{0}^{\frac{\pi }{3}}{\left( {{\tan }^{2}}x+x \right)\sin xdx}$

 $= \displaystyle\int\limits_{0}^{\frac{\pi }{3}} \left( \dfrac{\sin ^2x}{\cos ^2x}+x \right)\sin xdx$
$= \displaystyle\int\limits_{0}^{\frac{\pi }{3}} \dfrac{1-\cos ^2 x}{\cos ^2 x}\sin x dx+ \displaystyle\int\limits_{0}^{\frac{\pi }{3}}x\sin xdx$