$I= \int\limits_{\pi }^{2\pi} \frac{e^{x}cosx +(2x+1)e^{x}sinx+2x^{2}+1}{x+e^{x}sinx}dx$ $=\int\limits_{\pi}^{2\pi} \frac{e^{x}cosx+e^{x}sinx+1}{x+e^{x}sinx}dx + \int\limits_{\pi}^{2\pi} \frac{2x^{2}+2x.e^{x}sinx}{x+e^{x}sinx}$
$=ln|e^{x}sinx+x| + x^{2} $rồi thế cận nhưng ko ra :((