To tackle the integral , we can employ substitution. Let ; then, the derivative can provide a pathway forward. This substitution transforms our integral into a more manageable form that relates the polynomial factor to the exponential factor.

Next, remember to re-express everything in terms of and use integration techniques suitable for the resulting function. Often, thinking creatively with substitutions or even evaluating special cases aids in solving complex integrations. Keep an eye out for integrals that may hint at standard forms, as they can sometimes lead to quick resolutions or simplifications.

Happy integrating, and don’t forget to check your work for any possible constants or limits if it’s a definite integral!