Question

What is the integral of `f(x)=xe^(2x)`?

Answer 1

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 you can choose:
`f(x)=e^(2x)`
`g(x)=x`

`intxe^(2x)dx=xe^(2x)/2-int1*e^(2x)/2dx=`
`=xe^(2x)/2-e^(2x)/4+c`

Hope it helps