$\int e^x\cdot \cos x\mathrm dx$$=\int\cos x\mathrm d(e^x)$
$=e^x\cdot\cos x-\int e^x\mathrm d(\cos x)$
$=e^x\cos x+\int\sin x\cdot e^x \mathrm dx$
$=e^x\cos x+\int\sin x\mathrm d(e^x)$
$=e^x\cos x+\sin x\cdot e^x-\int e^x \mathrm d(\sin x)$
$=e^x(\cos x-\sin x)-\int e^x\cdot \cos x\mathrm dx $
$\Rightarrow \int e^x\cdot \cos x=\frac{e^x(\cos x+\sin x)}{2}$
Vậy $a=b=\frac 12$