An Alternative to Simpson?

(ax^4+bx+c)^-1

Will this function integrate, or am I stuck with Simpsons rule? (It's 35 years since I did my calculus, and I'm getting a bit rusty at it.)

This is what Wolfram gets...

integral[1/(a*x^4 + b*x + c)] - Wolfram|Alpha

Thanks, Prove it, I needn't feel quite so embarrassed about not being able to solve that lot for myself. I think Simpson will be just fine!