$\Leftrightarrow \frac{1}{2}\int\limits_{0}^{\pi }e^xdx+\frac{1}{2}\int\limits_{0}^{\pi }cos2x.e^xdx$xét $J=\int\limits_{0}^{\pi }cos2x.e^xdx=\int\limits_{0}^{\pi }cos2x.d(e^x)$$\Leftrightarrow e^xcos2x-\int\limits_{0}^{\pi }e^xd(cos2x)$$\Leftrightarrow e^xcos2x+2\int\limits_{0}^{\pi }e^xsin2x.dx$$\Leftrightarrow e^xcos2x+2e^xsin2x-2\int\limits_{0}^{\pi }e^xd(sin2x)$$\Leftrightarrow e^xcos2x+2e^xsin2x+4\int\limits_{0}^{\pi }cos2x.e^xdx$Ta có: $J= e^xcos2x+2e^xsin2x+4\int\limits_{0}^{\pi }cos2x.e^xdx$$\Leftrightarrow\int\limits_{0}^{\pi }cos2x.e^xdx=e^xcos2x+2e^xsin2x+4\int\limits_{0}^{\pi }cos2x.e^xdx$$\Leftrightarrow\int\limits_{0}^{\pi }cos2x.e^xdx=-\frac{1}{3}(e^xcos2x+2e^xsin2x)$$\Rightarrow \int\limits_{0}^{\pi }cos^2x.e^xdx=\frac{1}{2}e^x|^{\pi }_0-\frac{1}{6}(e^xcos2x+2e^xsin2x)|^{\pi }_0$
$\Leftrightarrow \frac{1}{2}\int\limits_{0}^{\pi }e^xdx+\frac{1}{2}\int\limits_{0}^{\pi }cos2x.e^xdx$xét $J=\int\limits_{0}^{\pi }cos2x.e^xdx=\int\limits_{0}^{\pi }cos2x.d(e^x)$$\Leftrightarrow e^xcos2x-\int\limits_{0}^{\pi }e^xd(cos2x)$$\Leftrightarrow e^xcos2x+2\int\limits_{0}^{\pi }e^xsin2x.dx$$\Leftrightarrow e^xcos2x+2e^xsin2x-2\int\limits_{0}^{\pi }e^xd(sin2x)$$\Leftrightarrow e^xcos2x+2e^xsin2x+4\int\limits_{0}^{\pi }cos2x.e^xdx$Ta có: $J= e^xcos2x+2e^xsin2x+4\int\limits_{0}^{\pi }cos2x.e^xdx$$\Leftrightarrow\int\limits_{0}^{\pi }cos2x.e^xdx=e^xcos2x+2e^xsin2x+4\int\limits_{0}^{\pi }cos2x.e^xdx$$\Leftrightarrow\int\limits_{0}^{\pi }cos2x.e^xdx=-\frac{1}{5}(e^xcos2x+2e^xsin2x)$$\Rightarrow \int\limits_{0}^{\pi }cos^2x.e^xdx=\frac{1}{2}e^x|^{\pi }_0-\frac{1}{10}(e^xcos2x+2e^xsin2x)|^{\pi }_0$
$\Leftrightarrow \frac{1}{2}\int\limits_{0}^{\pi }e^xdx+\frac{1}{2}\int\limits_{0}^{\pi }cos2x.e^xdx$xét $J=\int\limits_{0}^{\pi }cos2x.e^xdx=\int\limits_{0}^{\pi }cos2x.d(e^x)$$\Leftrightarrow e^xcos2x-\int\limits_{0}^{\pi }e^xd(cos2x)$$\Leftrightarrow e^xcos2x+2\int\limits_{0}^{\pi }e^xsin2x.dx$$\Leftrightarrow e^xcos2x+2e^xsin2x-2\int\limits_{0}^{\pi }e^xd(sin2x)$$\Leftrightarrow e^xcos2x+2e^xsin2x+4\int\limits_{0}^{\pi }cos2x.e^xdx$Ta có: $J= e^xcos2x+2e^xsin2x+4\int\limits_{0}^{\pi }cos2x.e^xdx$$\Leftrightarrow\int\limits_{0}^{\pi }cos2x.e^xdx=e^xcos2x+2e^xsin2x+4\int\limits_{0}^{\pi }cos2x.e^xdx$$\Leftrightarrow\int\limits_{0}^{\pi }cos2x.e^xdx=-\frac{1}{
3}(e^xcos2x+2e^xsin2x)$$\Rightarrow \int\limits_{0}^{\pi }cos^2x.e^xdx=\frac{1}{2}e^x|^{\pi }_0-\frac{1}{
6}(e^xcos2x+2e^xsin2x)|^{\pi }_0$