Nice Mathematical Trick: How can you tackle difficult Gaussian type integration

Following the mathematical integration that I posted few days ago, I want to give you a solution here. You will see how you can solve this type of problems considering 'constant' as a 'variable'. You may see the application of this type of integrations in Quantum mehanics a lot. Okay, look at the following picture:

In internet, you will see so many videos of gaussian integral (no x on the left side). One you may find here. But problem creates when there is even power of x on the left side of exponential as odd powers give directly zero because of being odd integral.

Anyway, I was also thinking how can I solve this problems for a long time. Few days ago, when I discovered it I did not want to wait to present it to my followers.

In the same way, we can do for x^4, x^6 ...etc.

In this way, you can solve all difficult Gaussian-type integral for even powers of x. Look it is very interesting as we never like to play with constant in integration or differentiation, but sometimes they may come up in main part of the problem and help us to solve it quite easily. You may remember this trick and give it to your friends who feel proud of his knowldge of mathematics :P .