Evaluate the following integral: `int_0^(pi//4)e^x sin x\ dx`

Explanation

Given:`int_0^(pi//4)e^x sin x\ dx`

`I=int_0^(pi//4)e^x sin x\ dx`

`I=[sinx e^x]_0^(pi/4)-int_0^(pi/4) cosx e^x dx`

`I=[sin(pi/4)e^(pi/4)-(sin0)e^0]-int_0^(pi/4) cosx e^x dx`

`I=[(1/(sqrt2) e^(pi/4))-0]-[cosxe^x]_0^(pi/4)-int_0^(pi/4) e^x (-sin x)dx`

`I=(1/(sqrt2))e^(pi/4)-[(cos(pi/4)e^(pi/4))-(cos0 e^0)+int_0^(pi/4) e^xsinxdx]`

`I=(e^(pi/4))/(sqrt2)-(e^(pi/4))/(sqrt2)+1-int_0^(pi/4) e^x sin x\dx`

`I=(e^(pi/4))/(sqrt2)-(e^(pi/4))/(sqrt2)+1-I`

...