Question

How do you integrate `e^2xcosx dx`?

Answer 1

Starting from:
`inte^2xcos(x)dx=` I would take the constant `e^2` out of the integral:
`e^2intxcos(x)dx=` then I would use integration by parts where you have:
`intf(x)*g(x)dx=F(x)g(x)-intF(x)g'(x)dx`
Where:
`F(x)=intf(x)dx`
`g'(x)` is the derivative of `g(x)`

In your case choosing `g(x)=x` you get:

`e^2[x*sin(x)-intsin(x)*1dx]=`
`e^2[xsin(x)+cos(x)]+c`

hope it helps