Question

What is the integral of `xe^2x dx`?

Answer 1

I am not sure that your integrand is right because you can simply write it as `e^2*x^2dx` and it can be integrated as (`e^2` is a constant):
`inte^2*x^2dx=e^2intx^2dx=e^2x^3/3+c`

On the other hand, it can be:
`intx*e^(2x)dx=` which can be solved By Parts:
`=x*e^(2x)/2-int1*e^(2x)/2dx=`
`=xe^(2x)/2-e^(2x)/4+c`