Evaluate the following integral ∫_0^(π/2)〖e^x (sin⁡x+cos⁡x ) 〗 dx

I=∫_0^(π/2)〖e^x  sin⁡x dx〗+∫_0^(π/2)〖e^x  cos⁡x 〗 dx
Let   u=e^x                     dv=sin⁡x dx
       du=e^x dx               v=-cos⁡x
∴I_1=-├ e^x  cos⁡x ┤|_0^(π/2)+∫_0^(π/2)〖e^x  cos⁡x 〗 dx=e^(π/2)+I_2
u=e^x                     dv=cos⁡x dx
 du=e^x dx               v=sin⁡x
∴I_1=e^(π/2)+├ e^x  sin⁡x ┤|_0^(π/2)-I_1=2e^(π/2)-I_1   
∴I_1=e^(π/2)
Also:
I_2=├ e^x  sin⁡x ┤|_0^(π/2)-∫〖e^x  sin⁡x 〗 dx=e^(π/2)-e^(π/2)=0
∴I=e^(π/2)