I tried using integration by parts but it just seems to get more complicated regardless of which function I set for f(x) or g(x). Here is the integral:
Here is one way to tackle it.
Since the e term is a product of a polynomial, x^2, we can try this:
..............[1]
Use the product rule on the left side and get:
Equate coefficients:
Solving the system results in:
Sub them back into [1]:
Integrate both sides and get:
There she is.